Question 5

A body of mass 2 kg begins to move under the action of a time dependent force given by $$\vec{F} = (6t)\hat{i} + (6t^2)\hat{j}$$ N. The power developed by the force at the time $$t$$ is given by:

$$\vec{F}=(6t)\hat{i}+(6t^2)\hat{j}$$. $$m=2$$ kg. $$\vec{a}=\vec{F}/m=(3t)\hat{i}+(3t^2)\hat{j}$$.

$$\vec{v}=\int\vec{a}dt=\frac{3t^2}{2}\hat{i}+t^3\hat{j}$$.

Power: $$P=\vec{F}\cdot\vec{v}=(6t)(3t^2/2)+(6t^2)(t^3)=9t^3+6t^5$$.

The answer is Option (4): $$(9t^3+6t^5)$$ W.

Create a FREE account and get:

Download resources