Cambridge IGCSE · 0625

Physics

Motion, forces and energy — Topic 1

Name: ____________________Date: October 10, 2026

1.
A cyclist increases speed uniformly from 4.0 m/s to 10.0 m/s in 3.0 s. Calculate the acceleration and the distance travelled during this time.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Uniform acceleration means the speed changes by equal amounts in equal times. The increase is 10.0 - 4.0 = 6.0 m/s over 3.0 s.
2. Acceleration = (v - u)/t = 6.0/3.0 = 2.0 m/s². The squared seconds distinguish acceleration from speed.
3. For uniform acceleration, mean speed = (u + v)/2 = 7.0 m/s, so distance = 7.0 × 3.0 = 21 m. Check with ut + ½at² = 12 + 9 = 21 m.
Marking points
- Uses acceleration = change in velocity ÷ time.
- Obtains acceleration = 2.0 m/s².
- Uses average speed = (4.0 + 10.0) ÷ 2 = 7.0 m/s.
- Obtains distance = 21 m.
Examiner tip: Uniform acceleration allows the arithmetic mean speed to be used.
2.
A motor lifts a 240 N load vertically through 5.0 m in 8.0 s. Calculate the work done and the useful power output.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses work done = force × distance. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Obtains work done = 1200 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Uses power = work done ÷ time. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains useful power = 150 W. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Keep joules for work and watts for power.
Marking points
- Uses work done = force × distance.
- Obtains work done = 1200 J.
- Uses power = work done ÷ time.
- Obtains useful power = 150 W.
Examiner tip: Keep joules for work and watts for power.
3.
A resultant force of 15 N acts on a 3.0 kg trolley. Calculate its acceleration.
[2 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses a = F/m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Obtains a = 5.0 m/s². Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Resultant force means the net force after all opposing forces (e.g. friction) have been accounted for.
Marking points
- Uses a = F/m.
- Obtains a = 5.0 m/s².
Examiner tip: Resultant force means the net force after all opposing forces (e.g. friction) have been accounted for.
4.
A 0.50 kg ball moving at 8.0 m/s collides with a stationary 1.5 kg ball and they stick together. Calculate their common velocity after the collision, using conservation of momentum.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates initial momentum = 0.50 × 8.0 = 4.0 kg m/s. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: States total mass after collision = 0.50 + 1.5 = 2.0 kg. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Uses conservation of momentum: total momentum before = total momentum after. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains common velocity = 4.0 ÷ 2.0 = 2.0 m/s. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: In a collision where objects stick together, momentum is conserved but kinetic energy is not — never assume the ball's original speed is simply shared.
Marking points
- Calculates initial momentum = 0.50 × 8.0 = 4.0 kg m/s.
- States total mass after collision = 0.50 + 1.5 = 2.0 kg.
- Uses conservation of momentum: total momentum before = total momentum after.
- Obtains common velocity = 4.0 ÷ 2.0 = 2.0 m/s.
Examiner tip: In a collision where objects stick together, momentum is conserved but kinetic energy is not — never assume the ball's original speed is simply shared.
5.
A stone of mass 0.20 kg is dropped from a height of 5.0 m. Calculate its speed just before hitting the ground, using energy conservation. Use g = 10 m/s².
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Develop this part of the answer: States that loss in gravitational potential energy equals gain in kinetic energy. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: Calculates GPE lost = mgh = 0.20 × 10 × 5.0 = 10 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Sets (1/2)mv² = 10 and rearranges for v². Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains v = 10 m/s. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Energy conservation avoids needing the time of fall — it directly links height dropped to final speed for any free-falling object.
Marking points
- States that loss in gravitational potential energy equals gain in kinetic energy.
- Calculates GPE lost = mgh = 0.20 × 10 × 5.0 = 10 J.
- Sets (1/2)mv² = 10 and rearranges for v².
- Obtains v = 10 m/s.
Examiner tip: Energy conservation avoids needing the time of fall — it directly links height dropped to final speed for any free-falling object.
6.
State Newton's third law of motion, and use it to explain the forces acting when a swimmer pushes against the water to move forward.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States Newton's third law: for every action force, there is an equal and opposite reaction force. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that the swimmer pushes water backward (the action force). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the water pushes the swimmer forward with an equal and opposite reaction force, propelling them through the water. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Action and reaction forces always act on two different objects, never on the same object, and are always equal in magnitude.
Marking points
- States Newton's third law: for every action force, there is an equal and opposite reaction force.
- States that the swimmer pushes water backward (the action force).
- States that the water pushes the swimmer forward with an equal and opposite reaction force, propelling them through the water.
Examiner tip: Action and reaction forces always act on two different objects, never on the same object, and are always equal in magnitude.
7.
A spring has an unstretched length of 12 cm. When a 4.0 N force is applied, it stretches to 16 cm. Calculate the spring constant.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates the extension: 16 − 12 = 4 cm = 0.04 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Uses k = F/extension. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains k = 4.0/0.04 = 100 N/m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Hooke's law uses extension (the change in length), not the total stretched length — always subtract the original length first.
Marking points
- Calculates the extension: 16 − 12 = 4 cm = 0.04 m.
- Uses k = F/extension.
- Obtains k = 4.0/0.04 = 100 N/m.
Examiner tip: Hooke's law uses extension (the change in length), not the total stretched length — always subtract the original length first.
8.
Explain, in terms of momentum, why a car's crumple zone reduces injury to passengers during a collision.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the crumple zone increases the time taken for the car (and passengers) to change momentum (decelerate to a stop) during the collision. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: States that force = change in momentum ÷ time, so for the same momentum change, a longer time reduces the force experienced. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: States that this reduced force on the passengers reduces the severity of injury. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Any safety feature that 'increases collision time' (crumple zones, airbags, seatbelts with give) works by the same principle: reducing the rate of momentum change reduces force.
Marking points
- States that the crumple zone increases the time taken for the car (and passengers) to change momentum (decelerate to a stop) during the collision.
- States that force = change in momentum ÷ time, so for the same momentum change, a longer time reduces the force experienced.
- States that this reduced force on the passengers reduces the severity of injury.
Examiner tip: Any safety feature that 'increases collision time' (crumple zones, airbags, seatbelts with give) works by the same principle: reducing the rate of momentum change reduces force.
9.
A crane lifts a 500 kg load through a vertical height of 12 m in 20 s. Calculate the useful power developed by the crane. Use g = 10 m/s².
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates the weight lifted: 500 × 10 = 5000 N. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Uses work done = force × distance = 5000 × 12. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains work done = 60 000 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Uses power = work ÷ time = 60 000 ÷ 20 = 3000 W. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Weight (a force, in newtons) must be calculated from mass using g before it can be used in the work-done formula.
Marking points
- Calculates the weight lifted: 500 × 10 = 5000 N.
- Uses work done = force × distance = 5000 × 12.
- Obtains work done = 60 000 J.
- Uses power = work ÷ time = 60 000 ÷ 20 = 3000 W.
Examiner tip: Weight (a force, in newtons) must be calculated from mass using g before it can be used in the work-done formula.
10.
A car of mass 1200 kg travelling at 20 m/s brakes and comes to rest, decelerating uniformly over 40 m. Calculate the braking force, using the work-energy relationship.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates the initial kinetic energy: (1/2) × 1200 × 20² = 240 000 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Develop this part of the answer: States that the work done by the braking force equals the kinetic energy lost (the car comes to rest). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Work through this mathematical step: Uses work done = force × distance, so 240 000 = force × 40. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains braking force = 6000 N. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Equating work done to kinetic energy change is a powerful shortcut that avoids needing to calculate the deceleration or time separately.
Marking points
- Calculates the initial kinetic energy: (1/2) × 1200 × 20² = 240 000 J.
- States that the work done by the braking force equals the kinetic energy lost (the car comes to rest).
- Uses work done = force × distance, so 240 000 = force × 40.
- Obtains braking force = 6000 N.
Examiner tip: Equating work done to kinetic energy change is a powerful shortcut that avoids needing to calculate the deceleration or time separately.
11.
A block of aluminium has a mass of 540 g and a volume of 200 cm³. Calculate its density.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States density = mass ÷ volume. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes 540 ÷ 200. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains density = 2.7 g/cm³. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Density does not depend on the amount of material — a small and a large block of the same pure substance have the same density.
Marking points
- States density = mass ÷ volume.
- Substitutes 540 ÷ 200.
- Obtains density = 2.7 g/cm³.
Examiner tip: Density does not depend on the amount of material — a small and a large block of the same pure substance have the same density.
12.
A brick of weight 24 N rests on the ground, with a base area of 0.03 m². Calculate the pressure it exerts on the ground.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses pressure = force ÷ area. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes 24 ÷ 0.03. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains pressure = 800 Pa. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: For the same force, spreading it over a larger area always reduces the pressure exerted.
Marking points
- Uses pressure = force ÷ area.
- Substitutes 24 ÷ 0.03.
- Obtains pressure = 800 Pa.
Examiner tip: For the same force, spreading it over a larger area always reduces the pressure exerted.
13.
A uniform beam is pivoted at its centre. A weight of 20 N hangs 1.5 m to the left of the pivot. Calculate the distance from the pivot at which a 30 N weight must be hung on the right for the beam to balance.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Develop this part of the answer: States the principle of moments: for equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the pivot. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: Calculates the moment of the 20 N weight: 20 × 1.5 = 30 N m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Sets 30 = 30 × d. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains d = 1.0 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Moment = force × perpendicular distance from the pivot; always identify the pivot first before calculating moments.
Marking points
- States the principle of moments: for equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the pivot.
- Calculates the moment of the 20 N weight: 20 × 1.5 = 30 N m.
- Sets 30 = 30 × d.
- Obtains d = 1.0 m.
Examiner tip: Moment = force × perpendicular distance from the pivot; always identify the pivot first before calculating moments.
14.
A distance-time graph for a cyclist shows: a straight line rising steadily from 0-5 s, a horizontal line from 5-10 s, then a straight line rising more steeply than the first section from 10-15 s. Describe the cyclist's motion in each of the three sections.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that from 0-5 s the cyclist travels at a constant (steady) speed. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that from 5-10 s the cyclist is stationary (at rest), since the distance does not change. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that from 10-15 s the cyclist travels at a greater constant speed than in the first section, since the line is steeper. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: On a distance-time graph, the gradient represents speed: a horizontal line means the object is stationary, and a steeper line means a greater speed.
Marking points
- States that from 0-5 s the cyclist travels at a constant (steady) speed.
- States that from 5-10 s the cyclist is stationary (at rest), since the distance does not change.
- States that from 10-15 s the cyclist travels at a greater constant speed than in the first section, since the line is steeper.
Examiner tip: On a distance-time graph, the gradient represents speed: a horizontal line means the object is stationary, and a steeper line means a greater speed.
15.
The speed-time graph for a car shows its speed increasing uniformly from 0 to 20 m/s in 8.0 s, then remaining constant at 20 m/s for a further 12 s. Calculate (a) the acceleration during the first 8.0 s, and (b) the total distance travelled in the 20 s.
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses acceleration = change in speed ÷ time. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Obtains acceleration = 20 ÷ 8.0 = 2.5 m/s². Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: States that distance travelled equals the area under the speed-time graph. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Work through this mathematical step: Calculates the area: (½ × 8.0 × 20) + (12 × 20). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Work through this mathematical step: Obtains total distance = 320 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Split the speed-time graph into a triangle and a rectangle and add their areas separately — this avoids errors in complex shapes.
Marking points
- Uses acceleration = change in speed ÷ time.
- Obtains acceleration = 20 ÷ 8.0 = 2.5 m/s².
- States that distance travelled equals the area under the speed-time graph.
- Calculates the area: (½ × 8.0 × 20) + (12 × 20).
- Obtains total distance = 320 m.
Examiner tip: Split the speed-time graph into a triangle and a rectangle and add their areas separately — this avoids errors in complex shapes.
16.
A skydiver jumps from an aircraft and falls, eventually reaching a constant maximum speed called terminal velocity, before opening their parachute. Explain, in terms of forces, why the skydiver's speed becomes constant.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that as speed increases, air resistance (drag) acting upward on the skydiver increases. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that eventually air resistance becomes equal in magnitude to the skydiver's weight, so the resultant force becomes zero. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that with zero resultant force there is no acceleration, so the skydiver falls at a constant speed (terminal velocity). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Terminal velocity is reached whenever resistive forces grow to exactly balance the driving force — the same principle applies to any object falling or moving through a fluid.
Marking points
- States that as speed increases, air resistance (drag) acting upward on the skydiver increases.
- States that eventually air resistance becomes equal in magnitude to the skydiver's weight, so the resultant force becomes zero.
- States that with zero resultant force there is no acceleration, so the skydiver falls at a constant speed (terminal velocity).
Examiner tip: Terminal velocity is reached whenever resistive forces grow to exactly balance the driving force — the same principle applies to any object falling or moving through a fluid.
17.
State the difference between a scalar quantity and a vector quantity, giving one example of each.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that a scalar quantity has magnitude only, with no direction, e.g. speed, mass or energy. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that a vector quantity has both magnitude and direction, e.g. velocity, force or displacement. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Speed and velocity are often confused: speed is a scalar (magnitude only) while velocity is a vector (speed in a stated direction).
Marking points
- States that a scalar quantity has magnitude only, with no direction, e.g. speed, mass or energy.
- States that a vector quantity has both magnitude and direction, e.g. velocity, force or displacement.
Examiner tip: Speed and velocity are often confused: speed is a scalar (magnitude only) while velocity is a vector (speed in a stated direction).
18.
A 2.0 kg trolley moving at 3.0 m/s to the right collides with a wall and rebounds at 1.0 m/s to the left. Taking the rightward direction as positive, calculate the change in momentum of the trolley.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Develop this part of the answer: Takes rightward direction as positive. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: Calculates momentum before collision = 2.0 × 3.0 = 6.0 kg m/s. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Calculates momentum after collision = 2.0 × (−1.0) = −2.0 kg m/s. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains change in momentum = −2.0 − 6.0 = −8.0 kg m/s (i.e. 8.0 kg m/s to the left). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: When an object rebounds, its velocity reverses direction — always assign a sign convention first so the reversal is captured correctly in the subtraction.
Marking points
- Takes rightward direction as positive.
- Calculates momentum before collision = 2.0 × 3.0 = 6.0 kg m/s.
- Calculates momentum after collision = 2.0 × (−1.0) = −2.0 kg m/s.
- Obtains change in momentum = −2.0 − 6.0 = −8.0 kg m/s (i.e. 8.0 kg m/s to the left).
Examiner tip: When an object rebounds, its velocity reverses direction — always assign a sign convention first so the reversal is captured correctly in the subtraction.
19.
An electric motor is supplied with 500 J of electrical energy and produces 350 J of useful kinetic energy output, the rest being wasted as heat. Calculate the efficiency of the motor.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States efficiency = (useful output energy ÷ total input energy) × 100%. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes (350 ÷ 500) × 100. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains efficiency = 70%. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Efficiency can never exceed 100%, since a machine cannot output more useful energy than it is supplied with.
Marking points
- States efficiency = (useful output energy ÷ total input energy) × 100%.
- Substitutes (350 ÷ 500) × 100.
- Obtains efficiency = 70%.
Examiner tip: Efficiency can never exceed 100%, since a machine cannot output more useful energy than it is supplied with.
20.
The gravitational field strength on the Moon is 1.6 N/kg, compared with 10 N/kg on Earth. An astronaut has a mass of 80 kg. Calculate the astronaut's weight on the Moon, and state what happens to the astronaut's mass.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses weight = mass × gravitational field strength. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Obtains weight on the Moon = 80 × 1.6 = 128 N. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: States that the astronaut's mass remains unchanged at 80 kg, since mass does not depend on gravitational field strength. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Mass is a fixed property of an object's matter and is the same everywhere in the universe; weight depends on the local gravitational field strength and varies from place to place.
Marking points
- Uses weight = mass × gravitational field strength.
- Obtains weight on the Moon = 80 × 1.6 = 128 N.
- States that the astronaut's mass remains unchanged at 80 kg, since mass does not depend on gravitational field strength.
Examiner tip: Mass is a fixed property of an object's matter and is the same everywhere in the universe; weight depends on the local gravitational field strength and varies from place to place.
21.
A spring with spring constant 150 N/m is compressed by 0.20 m. Calculate the elastic potential energy stored in the spring.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses elastic potential energy = ½ k x². Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes ½ × 150 × 0.20². Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains elastic potential energy = 3.0 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The extension or compression must be squared in this formula, so doubling the deformation quadruples the stored energy.
Marking points
- Uses elastic potential energy = ½ k x².
- Substitutes ½ × 150 × 0.20².
- Obtains elastic potential energy = 3.0 J.
Examiner tip: The extension or compression must be squared in this formula, so doubling the deformation quadruples the stored energy.
22.
A ball is whirled at a constant speed in a horizontal circle at the end of a string. State the direction of the resultant force acting on the ball, and explain why a resultant force is needed even though the ball's speed is not changing.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the resultant force acts towards the centre of the circle. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that although the ball's speed is constant, the direction of its velocity is continuously changing, so the ball is accelerating. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that a resultant force is required to produce this acceleration (change in direction), even though the speed itself stays constant. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Velocity is a vector, so a change in direction alone counts as acceleration, even with no change in speed — this is why circular motion always needs a centripetal (centre-seeking) force.
Marking points
- States that the resultant force acts towards the centre of the circle.
- States that although the ball's speed is constant, the direction of its velocity is continuously changing, so the ball is accelerating.
- States that a resultant force is required to produce this acceleration (change in direction), even though the speed itself stays constant.
Examiner tip: Velocity is a vector, so a change in direction alone counts as acceleration, even with no change in speed — this is why circular motion always needs a centripetal (centre-seeking) force.
23.
A car travels along a straight, level road at a constant velocity of 15 m/s. State what can be deduced about the resultant force acting on the car, and explain your reasoning.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the resultant force acting on the car is zero. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: Explains, using Newton's first law, that since the car moves at constant velocity it is not accelerating, and only a resultant force can cause acceleration. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Constant velocity (in both speed and direction) always means the resultant force is zero — this is Newton's first law.
Marking points
- States that the resultant force acting on the car is zero.
- Explains, using Newton's first law, that since the car moves at constant velocity it is not accelerating, and only a resultant force can cause acceleration.
Examiner tip: Constant velocity (in both speed and direction) always means the resultant force is zero — this is Newton's first law.
24.
A skier of mass 60 kg starts from rest and slides down a slope, descending a vertical height of 20 m. At the bottom, the skier's speed is 18 m/s. Calculate the kinetic energy gained and the energy lost to friction and air resistance. Use g = 10 m/s².
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates gravitational potential energy lost = mgh = 60 × 10 × 20 = 12 000 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Uses kinetic energy = ½mv². Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains kinetic energy gained = ½ × 60 × 18² = 9720 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: States that, by conservation of energy, energy lost to friction and air resistance = GPE lost − KE gained. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Work through this mathematical step: Obtains energy lost = 12 000 − 9720 = 2280 J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Whenever measured kinetic energy is less than the gravitational potential energy lost, the missing energy has been transferred to heat by resistive forces — energy is still conserved overall.
Marking points
- Calculates gravitational potential energy lost = mgh = 60 × 10 × 20 = 12 000 J.
- Uses kinetic energy = ½mv².
- Obtains kinetic energy gained = ½ × 60 × 18² = 9720 J.
- States that, by conservation of energy, energy lost to friction and air resistance = GPE lost − KE gained.
- Obtains energy lost = 12 000 − 9720 = 2280 J.
Examiner tip: Whenever measured kinetic energy is less than the gravitational potential energy lost, the missing energy has been transferred to heat by resistive forces — energy is still conserved overall.
25.
A 900 kg car decelerates uniformly from 20 m/s to rest in 4.0 s during an emergency stop. Calculate the average braking force acting on the car, using the impulse-momentum relationship.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates the change in momentum = 900 × (20 − 0) = 18 000 kg m/s. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Uses force = change in momentum ÷ time taken. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes 18 000 ÷ 4.0. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Obtains average braking force = 4500 N. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Force equals the rate of change of momentum — this form of Newton's second law applies even when mass stays constant and only velocity changes.
Marking points
- Calculates the change in momentum = 900 × (20 − 0) = 18 000 kg m/s.
- Uses force = change in momentum ÷ time taken.
- Substitutes 18 000 ÷ 4.0.
- Obtains average braking force = 4500 N.
Examiner tip: Force equals the rate of change of momentum — this form of Newton's second law applies even when mass stays constant and only velocity changes.