The diagram shows the displacement-time graph of a particle P which moves in a straight line such that, ts after leaving a fixed point O, its displacement from O is xm. On the axes below, draw the velocity-time graph of P.

1. (a)The diagram shows the displacement-time graph of a particle P which moves in a straight line such that, ts after leaving a fixed point O, its displacement from O is xm. On the axes below, draw the velocity-time graph of P.[3]
2. (b)(i)A particle Q moves in a straight line such that its velocity, v ms⁻¹, ts after passing through a fixed point O, is given by v = 3e⁻⁵ᵗ + (3t)/2, for t ≥ 0. Find the velocity of Q when t = 0.[1]
3. (b)(ii)Find the value of t when the acceleration of Q is zero.[3]
4. (b)(iii)Find the distance of Q from O when t = 0.5.[4]

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