A rocket prototype is fired from ground at time `t = 0` and it goes straight up. Take the launch point as origin and vertically upward direction as positive x direction. The acceleration of the rocket is given by
`a = (g)/(2) - kt^(2), 0 lt t le t_(0)`
`=- g, t gt t_(0)`
Where `t_(0) = sqrt((3g)/(2k))`
(a) Find maximum velocity of the rocket during the up journey.
(b) Find maximum height attained by the rocket.
(c) Find total time of flight.

Answer

(a) `V_(max) = sqrt((g^(3))/(18k))` (b) `X_(0) = (3g^(2))/(16k)` (c) `T = (3)/(2) sqrt((3g)/(2k))`