Q: A force $ \displaystyle \vec{F} = 3t\hat{i} + 5\hat{j}$ N acts on a body due to which its displacement varies as $\displaystyle \vec{S} = 2t^2\hat{i} – 5\hat{j}$ m. Work done by this force in 2 second is

(a) 32 J

(b) 24 J

(c) 46 J

(d) 20 J

Ans: (a)

Sol: $ \displaystyle \vec{dS} = 4 t dt \hat{i}$

$ \displaystyle W= \int_{0}^{t}\vec{F}.\vec{dS} $

$ \displaystyle W = \int_{0}^{2} (3t \hat{i}+ 5 \hat{j}).(4 t\hat{i})dt $

$\displaystyle W = \int_{0}^{2} 12 t^2 dt $

$ \displaystyle W = 12 [\frac{t^3}{3} ]_{0}^{2}$

$ \displaystyle W = 12 [\frac{2^3}{3} – 0]$

W = 32 J