A-LevelMathematicsMechanics9709/42 · Oct/Nov 2018 · Q37 Marks

The velocity of a particle moving in a straight line is vms¯¹ at time t seconds. The diagram shows a velocity-time graph which models the motion of the particle from t = 0 to t = T. The graph consists of four straight line segments. The particle reaches its maximum velocity V ms¯¹ at t = 10.

(i)Find the acceleration of the particle during the first 2 seconds.[1]
(ii)Find the value of V.[2]
(iii)At t = 6, the particle is instantaneously at rest at the point A. At t = T, the particle comes to rest at the point B. At t = 0 the particle starts from rest at a point one third of the way from A to B. Find the distance AB and hence find the value of T.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] Acceleration = -1 m s-2
[M1] [V/4 = 1 or (V + 2)/6 = 1] Use of gradient of line between t = 4 and t = 10 or use of similar triangles to find V
[A1] V = 4
[M1] [Distance = Area = ½ (6 + 2) × 2 = 8] Attempt distance travelled in first 6 seconds
[A1] Distance AB = 3 × 8 = 24 m
[M1] [½ × (T−6) × 4 = 24] Attempt to find the distance travelled from t = 6 to t = T and set up an equation for T
[A1] T = 18

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