The kinetic energy acquired by a mass m staring from rest under the action of a force `F = kt` is :

Options

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

Answer

C

Explanation

`F = kt`
`a = (kt)/(m)`
`underset(0)overset(v)int dv = (k)/(m) underset(0)overset(t)int t dt`
`v = (k)/(2m) t^(2)`
`K.E. + (1)/(2) mv^(2) = (1)/(2) m (k^(2)t^(4))/(4m^(2)) = (k^(2)t^(4))/(8m)`