A block of mass`2` kg is from to move along the x - axis it is at rest and from `1 = 0` onwards it is subjeted to a time - depended force `F(i) ` in the `x` diretion . The force `F(1) ` varies with `1` as shown in the figure . The kinetic of the block after `4.5` second is

Options

A. `4.50 J`
B. `7.50 J`
C. `5.06 J`
D. `14.06 J`

Answer

C

Explanation

If `u` is the final velocity, then change in momemtume `=` impulse `=` area enclosed by graph with time axis
`2(upsilon-0)=(4xx3)/(2)-(1)/(2)xx(3)/(2)xx2=4.5`
`:. upsilon=2.25 m//s`
`KE=(1)/(2)m upsilon^(2)=(1)/(2)xx2xx(2.25)^(2)=5.06J`