A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = (1/3) t2, where t is in s. Work done by the force in 2 s is :
Answer & explanation
Correct answer: option 3
Work-Energy theorem : W = \(\Delta\) K E
W = \(\frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2\)
Given : s = \(\frac{1}{3} t^2\)
⇒ v = \(\frac{ds}{dt} = \frac{2}{3}t\)
\(v_1 = v(t = 0) = 0 \text{ ; } v_2 = v(t = 2) = \frac{4}{3} m/s\)
∴ W = \(\frac{8}{3}\) J