A-LevelMathematicsMechanics9709/43 · May/June 2017 · Q36 Marks
A train travels between two stations, A and B. The train starts from rest at A and accelerates at a constant rate for T s until it reaches a speed of 25 m s⁻¹. It then travels at this constant speed before decelerating at a constant rate, coming to rest at B. The magnitude of the train's deceleration is twice the magnitude of its acceleration. The total time taken for the journey is 180 s.
- (i)Sketch the velocity-time graph for the train's journey from A to B.[1]
- (ii)Find an expression, in terms of T, for the length of time for which the train is travelling with constant speed.[2]
- (iii)The distance from A to B is 3300 m. Find how far the train travels while it is decelerating.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- B1 Trapezium, right-hand steeper than left-hand slope
- B1 Deceleration 0.5 T
- B1 Constant speed 180 – 1.5 T
- M1 Uses area property
- A1 T = 64
- B1 Distance decelerating = [0.5 × 32 × 25 =] 400 m
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