School / IB / PHYSICS HL / Special relativity Question practice
Special relativity About this practice Time dilation, length contraction and the invariance of the speed of light.
Physics: Higher Level Special relativity
View All Incomplete Complete Review mistakes One at a time
Revision Ladder All stages Easy Medium HardSoon
1 State the two postulates of Einstein's special theory of relativity. Easy 2 marks No calculator + 2 Marking analysis: A learner attempts the following task: “State the two postulates of Einstein's special theory of relativity.” Their response addresses only this point: “States that the laws of physics are the same in all inertial (non-accelerating) reference frames.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 3 Define proper time, and state which observer measures the proper time interval between two events. Easy 2 marks No calculator + 4 Marking analysis: A learner attempts the following task: “Define proper time, and state which observer measures the proper time interval between two events.” Their response addresses only this point: “Defines proper time as the time interval between two events measured by an observer for whom both events occur at the same location.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 5 A spacecraft clock measures a proper time interval of 10.0 s. The spacecraft moves at 0.80c relative to an observer on Earth. Calculate the time interval measured by the Earth observer, using the Lorentz factor γ = 1/√(1 − v²/c²). Medium 4 marks Calculator + 6 Marking analysis: A learner attempts the following task: “A spacecraft clock measures a proper time interval of 10.0 s. The spacecraft moves at 0.80c relative to an observer on Earth. Calculate the time interval measured by the Earth observer, using the Lorentz factor γ = 1/√(1 − v²/c²).” Their response addresses only this point: “Calculates the Lorentz factor: γ = 1/√(1 − 0.80²) = 1/√(0.36) = 1/0.6.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 7 Define proper length, and state what happens to the measured length of a moving object, as observed from a frame in which the object is moving. Easy 2 marks No calculator + 8 Marking analysis: A learner attempts the following task: “Define proper length, and state what happens to the measured length of a moving object, as observed from a frame in which the object is moving.” Their response addresses only this point: “Defines proper length as the length of an object measured in the reference frame in which the object is at rest.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 9 A spacecraft has a proper length of 120 m and travels at 0.60c relative to an observer on Earth. Calculate the length of the spacecraft as measured by the Earth observer. Medium 4 marks Calculator + 10 Marking analysis: A learner attempts the following task: “A spacecraft has a proper length of 120 m and travels at 0.60c relative to an observer on Earth. Calculate the length of the spacecraft as measured by the Earth observer.” Their response addresses only this point: “Calculates the Lorentz factor: γ = 1/√(1 − 0.60²) = 1/√(0.64) = 1/0.8 = 1.25.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 11 Explain why no object with mass can be accelerated to reach or exceed the speed of light, using the relativistic mass-energy relationship. Easy 3 marks No calculator + 12 Marking analysis: A learner attempts the following task: “Explain why no object with mass can be accelerated to reach or exceed the speed of light, using the relativistic mass-energy relationship.” Their response addresses only this point: “States that as an object's speed approaches c, the energy required to accelerate it further increases without bound.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 13 State Einstein's mass-energy equivalence relation, and calculate the energy equivalent of 1.0 g of mass. Use c = 3.00 × 10⁸ m s⁻¹. Easy 3 marks Calculator + 14 Marking analysis: A learner attempts the following task: “State Einstein's mass-energy equivalence relation, and calculate the energy equivalent of 1.0 g of mass. Use c = 3.00 × 10⁸ m s⁻¹.” Their response addresses only this point: “States E = mc².” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + 15 Two events occur simultaneously in the reference frame of observer A, but at different locations. Explain, using relativity of simultaneity, why observer B, moving relative to A, may not measure the two events as simultaneous. Easy 3 marks No calculator + 16 Marking analysis: A learner attempts the following task: “Two events occur simultaneously in the reference frame of observer A, but at different locations. Explain, using relativity of simultaneity, why observer B, moving relative to A, may not measure the two events as simultaneous.” Their response addresses only this point: “States that simultaneity (whether two events occur at the same time) is not absolute in special relativity — it depends on the observer's reference frame.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 17 A muon is created in the upper atmosphere and has a proper lifetime of 2.2 μs. Explain, using time dilation, how muons travelling close to the speed of light can be detected at the Earth's surface despite this short lifetime. Easy 2 marks No calculator + 18 Marking analysis: A learner attempts the following task: “A muon is created in the upper atmosphere and has a proper lifetime of 2.2 μs. Explain, using time dilation, how muons travelling close to the speed of light can be detected at the Earth's surface despite this short lifetime.” Their response addresses only this point: “States that from the Earth observer's frame, the muon's lifetime is time-dilated (appears longer) because the muon is moving at a speed close to c.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 19 Outline why, at everyday (non-relativistic) speeds, the effects of time dilation and length contraction are completely unnoticeable. Easy 2 marks No calculator + 20 Marking analysis: A learner attempts the following task: “Outline why, at everyday (non-relativistic) speeds, the effects of time dilation and length contraction are completely unnoticeable.” Their response addresses only this point: “States that for everyday speeds, v is extremely small compared to c, so v²/c² is extremely close to zero.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 21 A particle of mass 2.0 × 10⁻²⁷ kg moves at a speed of 0.90c. Calculate its relativistic momentum, given that the Lorentz factor at this speed is γ = 2.29. Use c = 3.00 × 10⁸ m s⁻¹. Medium 4 marks Calculator + 22 Marking analysis: A learner attempts the following task: “A particle of mass 2.0 × 10⁻²⁷ kg moves at a speed of 0.90c. Calculate its relativistic momentum, given that the Lorentz factor at this speed is γ = 2.29. Use c = 3.00 × 10⁸ m s⁻¹.” Their response addresses only this point: “Uses relativistic momentum p = γmv.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 23 A spacecraft moving at 0.50c relative to Earth fires a probe forward at a speed of 0.60c relative to the spacecraft. Using the relativistic velocity addition formula u = (v + u′)/(1 + vu′/c²), calculate the probe's speed relative to Earth, and explain why this is less than the value 1.10c predicted by simple (Galilean) addition. Medium 4 marks Calculator + 24 Marking analysis: A learner attempts the following task: “A spacecraft moving at 0.50c relative to Earth fires a probe forward at a speed of 0.60c relative to the spacecraft. Using the relativistic velocity addition formula u = (v + u′)/(1 + vu′/c²), calculate the probe's speed relative to Earth, and explain why this is less than the value 1.10c predicted by simple (Galilean) addition.” Their response addresses only this point: “Substitutes v = 0.50c and u′ = 0.60c into u = (v + u′)/(1 + vu′/c²), giving u = (0.50c + 0.60c)/(1 + 0.50 × 0.60).” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 25 In the 'twin paradox', one twin travels on a high-speed round trip to a distant star while the other twin remains on Earth. Explain why, upon reunion, the travelling twin is found to have aged less than the twin who stayed on Earth, and state why this is not a true paradox despite each twin seeing the other's clock as running slow during the trip. Medium 4 marks No calculator + 26 Marking analysis: A learner attempts the following task: “In the 'twin paradox', one twin travels on a high-speed round trip to a distant star while the other twin remains on Earth. Explain why, upon reunion, the travelling twin is found to have aged less than the twin who stayed on Earth, and state why this is not a true paradox despite each twin seeing the other's clock as running slow during the trip.” Their response addresses only this point: “States that, from Earth's frame, the travelling twin's clock runs slow (is time-dilated) throughout the journey due to their high speed.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks No calculator + 27 A particle has rest mass 1.67 × 10⁻²⁷ kg and moves with a Lorentz factor γ = 1.50. Calculate its total relativistic energy and its relativistic kinetic energy. Use c = 3.00 × 10⁸ m s⁻¹. Medium 5 marks Calculator + 28 Marking analysis: A learner attempts the following task: “A particle has rest mass 1.67 × 10⁻²⁷ kg and moves with a Lorentz factor γ = 1.50. Calculate its total relativistic energy and its relativistic kinetic energy. Use c = 3.00 × 10⁸ m s⁻¹.” Their response addresses only this point: “Calculates the rest energy: E₀ = mc² = 1.67 × 10⁻²⁷ × (3.00 × 10⁸)² ≈ 1.50 × 10⁻¹⁰ J.” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 5 marks Calculator + 29 A distant galaxy is moving away from Earth at a significant fraction of the speed of light. State and explain, using the relativistic Doppler effect, what happens to the observed wavelength of light received from this galaxy. Easy 3 marks No calculator + 30 Marking analysis: A learner attempts the following task: “A distant galaxy is moving away from Earth at a significant fraction of the speed of light. State and explain, using the relativistic Doppler effect, what happens to the observed wavelength of light received from this galaxy.” Their response addresses only this point: “States that the observed wavelength is increased (redshifted) compared to the wavelength emitted by the source.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + Self-assessed Not marked yet
Set total 94
This is a self-study tool, not a certified answer key or a predicted IB grade.
Loading progress Reset progress
Before you practise
Questions learners ask about this practice Are these official IB questions? No. These are original SubjectScout practice questions for Special relativity. They are not official past-paper questions or endorsed material.
What does this Physics: Higher Level practice page include? It includes selected topic questions, marking points, and feedback prompts designed to help learners practise before requesting teacher support.
Can I request a teacher for this exact topic? Yes. Tell SubjectScout the subject, exact topic, level and deadline, and the team will try to match you with a suitable verified teacher.
Unofficial content under accuracy, provenance, and rights review. Not affiliated with or endorsed by the International Baccalaureate Organization. Official past-paper questions are not reproduced here.
