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