A block of mass `2 kg` is free to move along the `x`-axis. It 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)` varies with `t` as shown in the figure. The kinetic energy of the block after `4.5` seconds is

Options

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

Answer

C

Explanation

Area under the F-t graph is equal to appled impulse on the block which is equal to change in its linear momentum .
Let `F_(0)` be the magnitude of maximum force in negative direction .
`(F_(0))/(1.5) = 4/3 rArr F_(0) = 2N `
Impulse = Area under the graph
`1/2 xx 4xx 3 - 1/2 xx2xx1.5 = 6-1.5 = 4.5 Ns `
Change in linear momentum = Impulse
Since initial momentum is zero hence change in momentum is same as final momentum (p)
`rArr p = 4.6 Ns`
Kinetic energy ` = (p^(2))/(2m) = (4.5 xx4.5)/(2xx2) =5.06 J `