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

Options

A. (a) `sqrtt`
B. (b) `t^(3//4)`
C. (c) `t^(3//2)`
D. (d) `t^2`

Answer

C

Explanation

Let us assume that the displacement of the body is directly proportional to `t^n`, i.e.,
`s=Kt^n`, `v=(ds)/(dt)=Knt^(n-1)`
and `a=(dv)/(dt)=Kn(n-1)t^(n-2)`
Force `F=ma=mKn(n-1)t^(n-2)`
Power, `P=Fv=[mKn(n-1)t^(n-2)][Knt^(n-1)]`
`=mKn^2(n-1)t^(2n-3)`
As power is constant, i.e. independent of time, hence
`2n-3=0` or `n=3/2` or `spropt^(3/2)`