Question

A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F}=(2\hat{i}+3t^2\hat{j})N$, where $\hat{i}$ and $\hat{j}$ are unit vectors along x and y axis. What power will be developed by the force at the time t ?

• A. $(2t^2+4t^4)W$
• B. $(2t^3+3t^4)W$
• C. $(2t^3+3t^5)W$
• D. $(2t^2+3t^3)W$

Answer 1

Answer: (C)

Applying Newton's second law of motion, acceleration, $\overrightarrow{a}=\frac{\overrightarrow{F}}{m}=2f+3t^{2j}$
Acceleration is defined as rate of change of velocity,
$<br/>\begin{array}{l}<br/>\vec{a}=\frac{d\vec{v}}{dt}\\ <br/>\vec{v}={\int }_0^t\vec{a}dt\\ <br/>\vec{v}={\int }_0^t\left(2{\hat{i}}^2+3t^2\hat{j}\right)dt\\ <br/>\vec{v}=t^2\hat{i}+t^{3\hat{j}}<br/>\end{array}<br/>$
Power, $P=\vec{F}\cdot \vec{v}=\left(2f\hat{i}+3t^2\hat{j}\right)\cdot \left(t^2\hat{i}+t^{3\hat{j}}\right)$
$<br/>P=\left(2t^3+3t^5\right)W<br/>$