A body is moved along a straight line by a machine delivering constant power . The distance moved by the body is time `t` is proptional to

Options

A. `t^(1//2)`
B. `t^(3//4)`
C. `t^(3//2)`
D. `t^(2)`

Answer

C

Explanation

`P = Fv = m a v = m((d v)/(d t)) v rArr (P)/(m)d t = v dv`
`rArr (P)/(m) xx t = (v^(2))/(2) rArr v = ((2P)/(m))^(1//2)(t)^(1//2)`
Now `s = int v d t = int ((2P)/(m))^(1//2) t^(1//2) d t`
`therefore s = ((2P)/(m))^(1//2)[(2t^(3//2))/(3)] rArr s prop t^(3//2)`