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9709 P42 - Mar 2019 - Q5
3377

The velocity of a particle moving in a straight line is \(v \text{ m s}^{-1}\) 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 \(3 \text{ m s}^{-2}\). The velocity of the particle at \(t = 5\) is \(7 \text{ m s}^{-1}\) 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 \(V \text{ m s}^{-1}\).

(i) Find the distance travelled by the particle in the first 8 s of its motion.

(ii) Given that when the particle comes to rest at \(t = 16\) its displacement from \(O\) is 32 m, find the value of \(V\).

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