AQA A-Level Physics: Displacement, Speed, Velocity, and Acceleration — mark scheme explained

The question

A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. Calculate the acceleration and the distance traveled during this time. [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

• S1

  1. Identify the given values: initial velocity (u) = 0 m/s, final velocity (v) = 20 m/s, time (t) = 5 s.

• S2

  2. Use the formula for acceleration: a = (v - u) / t

• S3

  3. Substitute the values: a = (20 - 0) / 5 = 4 m/s 2

• S4

  4. Use the formula for displacement: s = ut + (1/2)at 2

• S5

  5. Substitute the values: s = 0 × 5 + (1/2) × 4 × 5 2 = 50 m

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   1. Identify the given values: initial velocity (u) = 0 m/s, final velocity (v) = 20 m/s, time (t) = 5 s.

2. S2

   2. Use the formula for acceleration: a = (v - u) / t

3. S3

   3. Substitute the values: a = (20 - 0) / 5 = 4 m/s 2

4. S4

   4. Use the formula for displacement: s = ut + (1/2)at 2

5. S5

   5. Substitute the values: s = 0 × 5 + (1/2) × 4 × 5 2 = 50 m

6. Final answer: The acceleration is 4 m/s 2 and the distance traveled is 50 m.

Common mistakes

• Confusing displacement with distance — Always check if the question asks for distance or displacement. Displacement can be positive, negative, or zero, depending on the direction of movement relative to a reference point.
• Using average velocity instead of instantaneous velocity — Read the question carefully to determine if it asks for average or instantaneous velocity. Instantaneous velocity is the velocity at a specific moment in time, while average velocity is over an interval.
• Forgetting to include units in calculations — Always write down the units for each quantity used in your calculations and ensure that the final answer has the correct units. For example, velocity should be in m/s, acceleration in m/s 2 , and displacement in meters.
• Incorrectly interpreting the area under a velocity-time graph — Remember that the area under a velocity-time graph represents the displacement. The gradient (slope) of the graph gives the acceleration.
• Using the wrong formula for uniform acceleration — Memorize and understand the four main equations for uniform acceleration: v = u + at, s = (u + v)t / 2, s = ut + (1/2)at 2 , and v 2 = u 2 + 2as. Choose the appropriate equation based on the given information in the question.
• Neglecting the direction of acceleration — Always consider the direction of acceleration. For example, in free fall, the acceleration due to gravity (g) acts downwards and is therefore negative when using upward as the positive direction.
• Incorrectly identifying random and systematic errors in practical experiments — Understand that random errors can be reduced by taking multiple measurements and calculating an average, while systematic errors require calibration of equipment or a consistent method. Identify potential sources of error in the experiment and suggest specific ways to minimize them.

Where the marks go

• Full worked solution (all marking points)6 marks

Related questions

• AQA A-Level Physics: Fundamental and Derived Units in Physics — mark scheme explained →
• AQA A-Level Physics: Errors and Uncertainties in Measurements — mark scheme explained →