Physics - W.E.P. Question with Solution | TestHub

Given $\vec{F}=t\hat{i}+3t^2\hat{j}$ and $m=1\text{kg}$.

Acceleration $\vec{a}=\frac{\vec{F}}{m}=t\hat{i}+3t^2\hat{j}$

Velocity $\vec{v}=\int \vec{a}dt=\frac{t^2}{2}\hat{i}+t^3\hat{j}$ (since the body begins to move from rest, $\vec{v}(0)=0$).

At $t=2\text{s}$:

$\vec{F}=2\hat{i}+3(2{)}^2\hat{j}=2\hat{i}+12\hat{j}$

$\vec{v}=\frac{2^2}{2}\hat{i}+(2{)}^3\hat{j}=2\hat{i}+8\hat{j}$

Power $P=\vec{F}\cdot \vec{v}=(2\hat{i}+12\hat{j})\cdot (2\hat{i}+8\hat{j})$

$P=(2\times 2)+(12\times 8)=4+96=100\text{W}$

Answer: $100$