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)

$(2t^3 + 3t^5)W$

Answer 2

$\vec{F} = 2t \hat{i} + 3 t^2 \hat{j}$
$m \frac{d \vec{v}}{dt} = 2 t \hat{i} + 3 t^2 \hat{j}$ (m = 1 kg)
$\Rightarrow \, \int\limits^{\hat{v}}_0 d \vec{v} = \int\limits^t_0 (2t \hat{i} + 3 t^2 \hat{j}) dt \; \; \Rightarrow \, \vec{v} = t^2 \hat{i} + t^3 \hat{j}$
Power $= \vec{F}. \vec{v} = (2 t^3 + 3t^5) W$