Login/Sign Up
A body of mass $1 \mathrm{~kg}$ begins to move under the action of a time dependent force $\overrightarrow{\mathbf{F}}=\left(2 t \hat{\mathbf{i}}+3 \mathbf{t}^{2} \hat{\mathbf{j}}\right) \mathbf{N}$, where $\hat{\mathbf{i}}$ and $\hat{\mathbf{j}}$ are unit vectors along $\mathrm{x}$ and $y$ axis. What power will be developed by the force at the time t? A $\left(2 t^{2}+3 t^{3}\right) W$ B $\left(2 t^{2}+4 t^{4}\right) W$ C $\left(2 \mathrm{t}^{3}+3 \mathrm{t}^{4}\right) \mathrm{W}$ D $\left(2 t^{3}+3 t^{5}\right) W$
A body of mass $1 \mathrm{~kg}$ begins to move under the action of a time dependent force $\overrightarrow{\mathbf{F}}=\left(2 t \hat{\mathbf{i}}+3 \mathbf{t}^{2} \hat{\mathbf{j}}\right) \mathbf{N}$, where $\hat{\mathbf{i}}$ and $\hat{\mathbf{j}}$ are unit vectors along $\mathrm{x}$ and $y$ axis. What power will be developed by the force at the time t?
A $\left(2 t^{2}+3 t^{3}\right) W$
B $\left(2 t^{2}+4 t^{4}\right) W$
C $\left(2 \mathrm{t}^{3}+3 \mathrm{t}^{4}\right) \mathrm{W}$
D $\left(2 t^{3}+3 t^{5}\right) W$
Physics
A body of mass $1 \mathrm{~kg}$ begins to move under the action of a time dependent force $\overrightarrow{\mathbf{F}}=\left(2 t \hat{\mathbf{i}}+3 \mathbf{t}^{2} \hat{\mathbf{j}}\right) \mathbf{N}$, where $\hat{\mathbf{i}}$ and $\hat{\mathbf{j}}$ are unit vectors along $\mathrm{x}$ and $y$ axis. What power will be developed by the force at the time t?
A $\left(2 t^{2}+3 t^{3}\right) W$
B $\left(2 t^{2}+4 t^{4}\right) W$
C $\left(2 \mathrm{t}^{3}+3 \mathrm{t}^{4}\right) \mathrm{W}$
D $\left(2 t^{3}+3 t^{5}\right) W$

Correct Option D

Solution:
Given,

$\mathrm{F}=2 \mathrm{ti}+3 \mathrm{t}^{2}$

As we know,

$F=m a$
which can be represented as,

$F=m \frac{d v}{d t}$
Thus equating with given term and integrating,

$m \frac{d v}{d t}=2 t i+3 t^{2} j$

$\frac{d v}{d t}=\frac{2 t i+3 t^{2} j}{1}$

$\mathrm{v}=\frac{2 \mathrm{t}^{2}}{2} \mathrm{i}+\frac{3 \mathrm{t}^{3}}{3} \mathrm{j}$

According to formula,

$P=\vec{F} \cdot \vec{V}$
So,

$P=\left(2 t i+3 t^{2} j\right) \cdot\left(t^{2} i+t^{3} j\right)$
$P=\left(2 t^{3}+3 t^{5}\right) W$

i

More Material