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 is
(a)4.50 J
(b)7.50 J
(c)5.06 J
(d)14.06 J
Ans: (c)
Sol: Change in Momentum p = Area of F-t graph
$\large p = \frac{1}{2}(4\times 3) – \frac{1}{2}(1.5 \times 2)$
Kinetic Energy $\large K = \frac{p^2}{2 m}$
$\large K = \frac{(\frac{1}{2}(4\times 3) – \frac{1}{2}(1.5 \times 2))^2}{2 \times 2}$
= 5.06 J