Question

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 $F\left(t\right)$ in the $x$ direction. The force $F\left(t\right)$ varies with $t$ as shown in the figure. The kinetic energy of the block after $4.5$ second is :

Answer 1

Given,

$=-\frac{4}{3}$

at $t=4.5s\to F=-2N$

Total impulse,

$I=[\frac{1}{2}\times 3\times 4]-[\frac{1}{2}\times 2\times 1.5]=6-1.5=4.5SI.unit$

Impulse =change in momentum

$4.5=2[v-0]$

$v=\frac{4.5}{2}=2.25m/s$

$KE=\frac{1}{2}\times 2\times (2.25{)}^2=5.06J$