A variable force `F` acts on a body which is free to move. The displacement of the body is proportional to `t^(3)`, where `t` = time. The power delivered by `F` to the body will be proportional to

Options

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

Answer

C

Explanation

A variable ………………
Displacement `= s = kt^(3)` where `k` = constant.
`v = (ds)/(dt)=3kt^(2)` , `a =(dv)/(dt)=6kt`
`F= ma=6mkt`
Power `= Fv = 18mk^(2)t^(3)propt^(3)`.
`v =(ds)/(dt)= 3kt^(2)` , `a = (dv)/(dt) = 6kt`
`F = ma = 6kmt`
power `= Fv = 18mk^(2)t^(3)prop t^(3)`.