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^(1//4)`

Answer

C

Explanation

Here, power `P = F.v = (m (dv)/(dt)).v`
`rArr vdv = (P)/(m) dt`
Noe integrating,
`int_(0)^(v) vdv = (P)/(m) int_(0)^(t) dt`
`rArr (v^(2))/(2) = (Pt)/(m)`
or `v = ((2Pt)/(m))^((1)/(2))`
`rArr (dx)/(dt) = ((2P)/(m))^((1)/(2)) t^((1)/(2))`
`rArr dx =((2P)/(m))^((1)/(2))t^((1)/(2)) dt`
Integrating, we get
`underset(0) overset(x) int dx = ((2P)/(m))^((1)/(2)) underset(0) overset(t) int t^((1)/(2)) dt`
or `x = ((2P)/(m))^((1)/(2)) (t^((3)/(2)))/((3)/(2))` or `x prop t^((3)/(2))`.