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Q7. a. The displacement, S meters, of a body from a fixed point, is given by the equation:

S = 8t³ - 33t² + 45t where t is the time in seconds

Determine EACH of the following for this body:

i. Its initial velocity; (3)

ii. The time when it is at rest. (4)

iii. The time when its acceleration is 30 ms^{- 2} (3)

b. Determine dv/dt and (d² v)/(dt² ) for the function v = (1 - t⁴)/(1 - t² ) (6)