A block of mass $2 \mathrm{~kg}$ is free to move along the $x$-axis. It is at rest and from $t$ $=0$ onwards…
A block of mass $2 \mathrm{~kg}$ 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 $F(t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after $4.5 \mathrm{~s}$ is
$4.50 \mathrm{~J}$
$7.50 \mathrm{~J}$
$5.06 \mathrm{~J}$
$14.06 \mathrm{~J}$
Solution
Area under $F$ - $t$ graph $=$ momentum
$
\begin{aligned}
&=P=\sqrt{2 k m} \\
& \therefore \quad k=\frac{A^2}{2 m} \\
&(A=\text { net area of } F-t \text { graph) } \\
&=\frac{\left\{\left(\frac{4 \times 3}{2}\right)-\left(\frac{1.5 \times 2}{2}\right)\right\}^2}{2 \times 2}=5.0625 \mathrm{~J}
\end{aligned}
$
$\therefore$ The correct option is (c)
