A block of mass `2kg` is free to move along the x-axis. It is at rest and from `t=0` onwards, it is subjected to a time-dependent force `F(t)` in the x-direction. The force `F(t)` vaies with t as shown in figure. The kinetic energy of the block after `4.5s` is

Options

A. 3.50 J
B. 7.50 J
C. 5.06J
D. 14.06J

Answer

C

Explanation

The area under force time graph gives the change in momentum.
At t=0, block is at rest, so it means momentum at t=0 is zero. Let p is the momentum at t=4.5 s.
`p-0=1/2xx4xx3-1/2xx2xx1.5=4.5N-s`
KE at t=4.5s = `p^2/(2m)=((4.5)^2)/(2xx2)` =5.0625J = 5.06J