Work Power Energy Question 9
Question 9 - 2024 (31 Jan Shift 2)
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:
(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:
$\vec{F}=\left(6 t \hat{i}+6 t^{2} \hat{j}\right) N$
$\overrightarrow{\mathrm{F}}=\mathrm{ma}=\left(6 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^{2} \hat{\mathrm{j}}\right)$
$\vec{a}=\frac{\vec{F}}{m}=\left(3 t \hat{i}+3 t^{2} \hat{j}\right)$
$\overrightarrow{\mathrm{v}}=\int_{0}^{\mathrm{t}} \overrightarrow{\mathrm{a}} d \mathrm{t}=\frac{3 \mathrm{t}^{2}}{2} \hat{\dot{\mathrm{i}}}+\mathrm{t}^{3} \hat{\mathrm{j}}$
$\mathrm{P}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{v}}=\left(9 \mathrm{t}^{3}+6 \mathrm{t}^{5}\right) \mathrm{W}$
