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  4. A block of mass 2 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 s is

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Q. A block of mass $2\, kg$ 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 $4.5\, s$ isPhysics Question Image

IIT JEEIIT JEE 2010Work, Energy and Power

Solution:

Area under F-t graph = momentum
$=p=\sqrt{2 \, km}$
$\therefore k=\frac{A^2}{2m}$ ($A$ = net area of $F-t$ graph)
$ =\frac{ \left\{ \left(\frac{4 \times 3}{2}\right)-\left(\frac{1.5 \times2}{2}\right)\right\}^2}{2 \times 2}$
$5.0625\,J$