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

Answer

C

Explanation

P = Constant, `Prarr` Power
`implies` F.v = Constant `implies` mav = k
`implies m (dv)/(dt) v = k`
`intvdv = int(k/m) dt impliesv^2/2 =(k/m)t`
`implies v = ((2k)/m)^(1/2)t^(1/2)=k.t^(1/2)`
Now, `S = intvdt = intk.t^(1/2)dt`
`S=k.[(t^(1/2+1))/(1/2+1)]=2/3k..t^(3/2)`
`implies S prop t^(3/2)`