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

(c) area under `F-t` graph the impulse or the change in the linear momentum of the body . As the inity velocity (andtherefore the intial linearmomentum) of the body is zero , the are under `F -t` graph give the final linear momentum of the `deltaAOB`

`= (1)/(2) xx 3 xx 4 = 6N -s`
Also `(OA)/(OB) = (CD)/(CB)`
`rArr (4)/(5) = (CD)/(1.5)f`
`rArr CD = 2`
` :.` Area of `deltaBCD = -([(1)/(2) xx 1.5 xx 2]) = -1.5 N-s`
The final linear momentum `= 6 - 1.5 = 4.5 N-s`
Kinetic energy of the block ` = (p^(2))/(2m) = ((4.5)^(2))/(2 xx 2) = 5.061`