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 $F(t)$ in the $x$-direction. The force $F(t)$ varies with t as shown in the figure. The kinetic energy of the block after $4.5s$ is

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

Answer 1

Answer: (C)

Area under F-t graph = momentum
$=p=\sqrt{2km}$
$\therefore k=\frac{A^2}{2m}$ ($A$ = net area of $F-t$ graph)
$=\frac{{\left\{\left(\frac{4\times 3}{2}\right)-\left(\frac{1.5\times 2}{2}\right)\right\}}^2}{2\times 2}$
$5.0625J$