Question 56: Work, Energy and Power & Circular Motion

Question

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

Accepted Answer

$$\begin{aligned}
& \vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}ight) N \
& \vec{F}=m \vec{a}=\left(6 t \hat{i}+6 t^2 \hat{j}ight) \
& \vec{a}=\frac{\vec{F}}{m}=\left(3 t \hat{i}+3 t^2 \hat{j}ight) \
& \vec{v}=\int_\limits0^t \vec{a} d t=\frac{3 t^2}{2} \hat{i}+t^3 \hat{j} \
& P=\vec{F} \cdot \vec{v}=\left(9 t^3+6 t^5ight) W
\end{aligned}$$

Answer

$$\left(3 t^3+6 t^5\right) W$$

Answer

$$\left(9 t^5+6 t^3\right) W$$

Answer

$$\left(6 t^4+9 t^5\right) W$$

Answer

$$\left(9 t^3+6 t^5\right) W$$

Work, Energy and Power & Circular Motion

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

Choose the correct answer: