A particle of mass m at rest is acted upon by a force P for a time t. Its kinetic energy after an interval t is 

Options

A. `(P^2 t^2)/(m)`
B. `(P^2 t^2)/(2m)`
C. `(P^2 t^2)/(3m)`
D. `(Pt)/(2m)`

Answer

B

Explanation

Here , mass of the particle = m, force = P, time = t, initial velocity , u = 0
As `P = ma " "` (where a is the acceleration)
`:. a = P/m`
As `S = ut + 1/2 at^2`
`:. S = 0 xx t + 1/2 (P/m) t^2 " (Using (i))"`
or `S = 1/2 (Pt^2)/(m) " " ....(ii)`
According to work - energy theorem
Kinetic energy = `PS = P 1/2 (Pt^2)/m " (Using (ii))"`
`= (P^2t^2)/(2m)` .