A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Inertial Frames and Special Relativity Postulates — mark scheme explained
The short answer
The concept of an inertial frame of reference is fundamental to understanding Einstein's theory of special relativity. An inertial frame of reference is a coordinate system in which Newton's first law (the law of inertia) holds true.
The question
A spaceship is traveling at a speed of 0.8c relative to an observer on Earth. According to the observer on Earth, how much slower does a clock on the spaceship run compared to a clock on Earth?
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For questions involving calculations, ensure that all steps are shown clearly and that units are included in the final answer. For conceptual questions, provide clear and concise explanations, using examples where appropriate to illustrate your points.
What the command words demand
- Define
- Provide a precise definition of the term or concept.
- Explain
- Give a detailed account of how or why something happens, including relevant principles and examples.
- Calculate
- Perform a mathematical calculation to find a specific value, showing all steps clearly.
- Compare
- Identify similarities and differences between two or more concepts or phenomena.
- Describe
- Provide a detailed description of a phenomenon or process without necessarily explaining the underlying mechanisms.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 10-15 minutes for a question worth 6 marks. Ensure you have enough time to read the question carefully, plan your response, and check your work.
- Identify the relevant formula for time dilation: t' = t / √(1 - v 2 /c 2 )1 mark
- Substitute the given values into the formula: t' = t / √(1 - (0.8c) 2 /c 2 )1 mark
- Simplify the expression inside the square root: t' = t / √(1 - 0.64) = t / √0.36 = t / 0.61 mark
- Calculate the time dilation factor: t' = t / 0.6 ≈ 1.67t1 mark
- The clock on the spaceship runs slower by a factor of 1.67 compared to the clock on Earth.0 marks
Final answer: The clock on the spaceship runs slower by a factor of 1.67.
Work through every step correctly and you earn all 4 marks.
Another worked example
A rod is moving at a speed of 0.5c relative to an observer on Earth. The length of the rod in its rest frame is 10 meters. What is the observed length of the rod according to the observer on Earth?
- Identify the relevant formula for length contraction: L' = L √(1 - v 2 /c 2 )1 mark
- Substitute the given values into the formula: L' = 10 √(1 - (0.5c) 2 /c 2 )1 mark
- Simplify the expression inside the square root: L' = 10 √(1 - 0.25) = 10 √0.75 ≈ 10 × 0.8661 mark
- Calculate the observed length: L' ≈ 8.66 meters1 mark
Final answer: The observed length of the rod is approximately 8.66 meters.
Work through every step correctly and you earn all 4 marks.
Common mistakes
Confusing inertial frames with non-inertial frames
Why it happens: Students may not fully understand the distinction between inertial and non-inertial frames. Inertial frames are those in which Newton's first law holds, while non-inertial frames experience acceleration.
Fix: Emphasize that an inertial frame is one where objects at rest stay at rest and objects in motion move with constant velocity unless acted upon by a force. Non-inertial frames, such as a rotating or accelerating frame, do not satisfy this condition.
Misinterpreting the first postulate of special relativity
Why it happens: Students might think that the laws of physics are different in different inertial frames. The correct interpretation is that the form of physical laws remains the same.
Fix: Clarify that the first postulate means the equations and principles of physics look the same in all inertial frames, not that the outcomes of experiments will necessarily be identical.
Forgetting the invariance of the speed of light
Why it happens: Students may overlook the second postulate and assume that the speed of light can vary depending on the observer's motion.
Fix: Reinforce that the speed of light is always c (approximately 3 × 10 8 m/s) in all inertial frames, regardless of the relative motion of the source or observer.
Confusing time dilation with length contraction
Why it happens: Students might mix up the effects of time dilation and length contraction. Time dilation affects the passage of time, while length contraction affects the measurement of length.
Fix: Explain that time dilation causes moving clocks to run slower, and length contraction causes objects in motion to appear shorter in the direction of motion. Use specific examples to illustrate each effect.
Incorrectly applying the Lorentz factor
Why it happens: Students may make algebraic errors when calculating the Lorentz factor (γ = 1 / √(1 - v 2 /c 2 )) or misinterpret its significance.
Fix: Practice using the Lorentz factor in various contexts, such as time dilation and length contraction. Ensure students understand that γ is always greater than or equal to 1 and increases with velocity.
Failing to account for relativity of simultaneity
Why it happens: Students might assume that events simultaneous in one frame are also simultaneous in another, which is not always true.
Fix: Explain the concept of relativity of simultaneity and provide examples where events that are simultaneous in one frame are not simultaneous in another. Use spacetime diagrams to visualize this effect.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Time Dilation Calculation | Apply the time dilation formula to find how much slower a moving clock runs. | 4 |
| Length Contraction | Calculate the observed contracted length of a rod moving at relativistic speed. | 4 |
| Relativity Of Simultaneity | Find the time difference between two events in Earth's frame using Lorentz transformations. | 5 |
| Relativistic Time Dilation | Apply time dilation to find the distance a muon travels before decaying, as measured by a ground observer. | 6 |
| Total across these question types | 19 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.