A-LevelMathematicsMechanics9709/41 · Oct/Nov 2017 · Q47 Marks

The diagram shows the velocity-time graph of a particle which moves in a straight line. The graph consists of 5 straight line segments. The particle starts from rest at a point A at time t = 0, and initially travels towards point B on the line. [Figure 4.1]

(i)Show that the acceleration of the particle between t = 3.5 and t = 6 is −10 m s⁻².[1]
(ii)The acceleration of the particle between t = 6 and t = 10 is 7.5 m s⁻². When t = 10 the velocity of the particle is V m s⁻¹. Find the value of V.[2]
(iii)The particle comes to rest at B at time T s. Given that the total distance travelled by the particle between t = 0 and t = T is 100 m, find the value of T.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[B1] Acceleration = (-25) / 2.5 = -10 m s⁻² AG
[M1] V = -15 + 7.5 × 4 Using v-t graph OE
[A1] V = 15 m s⁻¹
[B1] Using v = 0 at t = 4.5 and t = 8
[M1] ½ x (4.5+ 2) × 10 + ½ × (8–4.5) × 15 + ½ × (T–8) × 15 = 100 Attempting to use area to find total distance travelled
[M1] For setting up an equation for total distance travelled and solving for T
[A1] T = 13.5

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