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11. A particle, P, moves on the x-axis. At time t seconds, the velocity of P is v ms¹ in the direction of positive x, where v is given by v=8 t-\frac{3}{2} t^{2}(\text { for } 0 \leq \mathrm{t} \leq 4) \text { and } v=16-2 t(\text { for } \mathrm{t}>4 \text { ) } When t = 0, P is at the origin, O. Find a) The greatest speed of P during the interval 0 ≤ t ≤ 4 b) The distance of P from O when t = 4. c) The time at which P is instantaneously at rest for t > 4. d) The total distance travelled by P during the first 10 seconds of it motion.

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