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. directly proportional to `t^(2)`
B. independent of `t`
C. directly proportional to `t^(4)`
D. directly proportional to `t`

Explanation

`f=kt`
`m int_(0)^(v)dv=k int_(0)^(t)tdt`
`mv=kt^(2)`
`v=(k)/(m)t^(2)`
`K.E.=(1)/(2)mv^(2)=(1)/(2)m(k^(2))/(m^(2))t^(4)=((k^(2))/(2m))t^(4)`
`KE prop t^(4)`