A-LevelMathematicsMechanics9709/42 · Feb/Mar 2019 · Q57 Marks

The velocity of a particle moving in a straight line is v m s⁻¹ at time t seconds after leaving a fixed point O. The diagram shows a velocity-time graph which models the motion of the particle from t = 0 to t = 16. The graph consists of five straight line segments. The acceleration of the particle from t = 0 to t = 3 is 3 m s⁻². The velocity of the particle at t = 5 is 7 m s⁻¹ and it comes to instantaneous rest at t = 8. The particle then comes to rest again at t = 16. The minimum velocity of the particle is V m s⁻¹.

(i)Find the distance travelled by the particle in the first 8 s of its motion.[3]
(ii)Given that when the particle comes to rest at t = 16 its displacement from O is 32 m, find the value of V.[4]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.

[B1] Velocity at t = 3 is 3 × 3 = 9
[M1] Attempt distance travelled in the first 8 seconds using Distance = area under graph. [½ × 3 × 9 + ½ (9 + 7) × 2 + ½ × 3 × 7]
[A1] Distance = 40 m
[M1] Use given displacement to set up equation for area of triangle or attempt to find distance or displacement from t = 8 to t = 16 [32 = 40 + area of triangle]
[A1] Area of triangle or displacement/distance = (-)8
[M1] Set up an equation for the area of triangle involving V or use suvat equations to set up an equation involving V [Distance = ½ × 8 × V = (-)8]
[A1] V = -2

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