AQA AS Level Physics Paper 2, June 2024: Question 23

1 mark · Medium difficulty · Multiple Choice

Calculate the displacement of a horse from point X after walking for 45 s on a circular track of circumference 60 m at a constant speed of 2.0 m s^-1.

Practise this question

Question

Multiple choice question 23 asking for the displacement of a horse walking on a circular track of circumference 60 m at 2.0 m s^-1 after 45 s. Options are A 19 m, B 30 m, C 38 m, and D 90 m, each with an answer box next to it.
Question text

23 A horse starts walking from point X on a circular track of circumference 60 m.

The speed of the horse is a constant 2.0 m s−1.

What is the horse’s displacement from X after 45 s?

[1 mark]

A 19 m

B 30 m

C 38 m

D 90 m

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer is A, corresponding to a displacement of 19 m.

23 A 19 m

How to answer it

Horse's Displacement on a Circular Track

AQA AS Level Physics • Mechanics

What this question tests

This question assesses your understanding of the fundamental vector distinction between distance (scalar) and displacement (vector). Specifically, it tests your ability to calculate total path length using speed and time, relate path length to the geometry of a circle, and determine straight-line displacement from a starting point.

Question 23: Multiple Choice Part (a)

AQA AS Level Physics Exam-Style Breakdown

✅ Correct Answer: A (19 m)

The correct option is A. Through proper step-by-step calculation of total distance travelled and application of chord length geometry across a circle, the displacement evaluates to 19 m.

Marks available: 1 mark

💡 Key Knowledge

  • Displacement: The shortest straight-line distance from the starting point to the final position, taking direction into account.
  • Distance vs. Displacement: Distance is total arc length travelled along the track; displacement is the straight chord connecting start and end points.
  • Geometry link: For a circular path, straight-line displacement corresponds to the chord length 2r sin(θ / 2) or drawing a triangle from the centre of the circle.

🧠 Exam Technique

Don't fall into the trap of assuming displacement is equal to total distance or simply subtracting full laps linearly. Always sketch a quick circular diagram, track where the object lands relative to the origin point X, and construct a triangle to find the direct chord length.

❌ Common Errors

  • Option D (90 m): Simply multiplying speed ( 2.0 m s⁻¹ ) by time ( 45 s ) to find the total distance travelled ( 90 m ), forgetting that distance is not displacement.
  • Option C (38 m): Doubling a radius or miscalculating the angle component directly without accounting for the correct fraction of a circle.

📐 Step-by-Step Calculation

  1. Calculate the total distance travelled by the horse:
    Distance = speed × time
    Distance = 2.0 m s⁻¹ × 45 s = 90 m
  2. Determine how many complete laps and remaining distance the horse completes:
    Circumference = 60 m .
    Number of laps = 90 m / 60 m = 1.5 laps .
    This means the horse travels 1 full lap plus half a lap ( 0.5 × 60 m = 30 m past point X).
  3. Relate the distance to the geometry of the circle:
    A half-lap means the horse finishes directly opposite point X on the circular track.
    Therefore, the straight-line displacement from X to the final position is equal to the diameter of the circular track.
  4. Calculate the radius ( r ) and diameter ( d ):
    Circumference C = 2 × π × r = 60 m
    Radius r = 60 / (2π) = 9.549 m
    Diameter d = 2 × r = 60 / π = 19.098 m
  5. Round to appropriate significant figures:
    Given values (like 2.0 m s⁻¹ and 60 m ) are to 2 significant figures. Rounding 19.098 m gives 19 m (Option A).

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.