Work Power Energy Question 9
Question 9 - 2024 (31 Jan Shift 2)
A body of mass $2 kg$ 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:
(1) $\left(6 t^{4}+9 t^{5}\right) W$
(2) $\left(3 t^{3}+6 t^{5}\right) W$
(3) $\left(9 t^{5}+6 t^{3}\right) W$
(4) $\left(9 t^{3}+6 t^{5}\right) W$
Show Answer
Answer: (4)
Solution:
$\vec{F}=\left(6 t \hat{i}+6 t^{2} \hat{j}\right) N$
$\overrightarrow{F}=ma=\left(6 t \hat{i}+6 t^{2} \hat{j}\right)$
$\vec{a}=\frac{\vec{F}}{m}=\left(3 t \hat{i}+3 t^{2} \hat{j}\right)$
$\overrightarrow{v}=\int _0^{t} \overrightarrow{a} d t=\frac{3 t^{2}}{2} \hat{\dot{i}}+t^{3} \hat{j}$
$P=\overrightarrow{F} \cdot \overrightarrow{v}=\left(9 t^{3}+6 t^{5}\right) W$
