Q:A particle moves with a velocity $\displaystyle \vec{v}= 5\hat{i} – 3\hat{j} + 6\hat{k} $ m/s under the influence of a constant force $\displaystyle \vec{F}= 10\hat{i} + 10\hat{j} + 20\hat{k}$ . The instantaneous power applied to the particle is:

(A) 200 J/s

(B) 40 J/s

(C) 140 J/s

(D) 170 J/s

Solution :

$ \displaystyle P = \vec{F}.\vec{v} $

$ \displaystyle = (10\hat{i} + 10\hat{j} + 20\hat{k}).(5\hat{i} – 3\hat{j} + 6\hat{k})$

= 50 – 30 + 120

= 140 J/s