A car of mass `M` accelerates starting from rest. Velocity of the car is given by `v=((2Pt)/(M))^((1)/(2))` where `P` is the constant power supplied by the engine. The position of car as a function of time is given as

Options

A. `((8P)/(9M))^((1)/(2)) t^((3)/(2))`
B. `((9P)/(8M))^((1)/(2)) t^((3)/(2))`
C. `((8P)/(9M))^((1)/(2))t^((2)/(3))`
D. `((9P)/(8M))t^(3)`

Answer

A

Explanation

Here `v =((2Pt)/(M))^((1)/(2))` or `(ds)/(dt) = ((2Pt)/(M))^((1)/(2))` or `ds = ((2Pt)/(M))^((1)/(2)) dt`. Inegrate to find 's'.