A particle of mass m is at rest. A force Facts upon it for time t. It acquires kinetic energy equal to

Options

A. `F^2t^2//2m`
B. `Ft//2m`
C. `(F^2)/(2mt^2)`
D. `t^2//2Fm`

Answer

A

Explanation

Kinetic energy = `1/2 mv^2 = 1/(2m) (m^2v^2)`
`=("(Momentum)"^2)/(2m)`
Momentum = Impulse
`KE = ("(impulse)"^2)/(2m) = (F^2 t^2)/(2m)`
(`because` Impuls = Force `xx` Time = Change in momentum)