The kinetic energy acquired by a mass `m` travelling a certain distance d, starting from rest, under the action of a force F such that the force F is directly proportional to t is

Options

A. (a) Directly proportional to `t^2`
B. (b) Independent of t
C. (c) Directly proportional to `t^4`
D. (d) Directly proportional to `t`

Answer

C

Explanation

`f=kt`
`m underset0oversetvintdv=kunderset0oversettintdt`
`mv=kt^2`
`v=k/mt^2`
`KE=1/2mv^2=1/2mk^2/m^2t^4=((k^2)/(2m))t^4`
`KEpropt^4`