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Q7. (a) The displacement s metres of a body from a fixed point is given by the equation:

s = 10/3 t³ – 33/2 t² + 20t + 6 where t is the time in seconds.

Determine EACH of the following for this body:

(i) its initial velocity; (3)

(ii) the times when it is at rest; (4)

(iii) the time when its acceleration is 7 ms^-2. (3)

(b) Given h = 4 – 3 sin t + 5cos t, where t is the time in seconds, evaluate.

h – dh/dt when t = 1 second (6)