The velocity of a body of mass 2 kg as a function of t is given by$ v(t)=2 t \hat{i}+t^{2} \hat{j} $Find the momentum and the force acting on it at time t = 2 sec.
The velocity of a body of mass 2 kg as a function of t is given by$ v(t)=2 t \hat{i}+t^{2} \hat{j} $Find the momentum and the force acting on it at time t = 2 sec.

m=2kg

$
\underset{v}{\rightarrow}(t)=2 t \hat{i}+t^{2} \hat{j}
$

$
\vec{v} \text { at } 2 \mathrm{sec}, \underset{v}{\vec{v}}(2 t)=2(2 t) \hat{i} 2^{2} \hat{j}, v(2)=4 \hat{i}+4 \hat{j}
$

$
\text { Momentum, } \underset{P}{\vec{P}}(2)=m \underset{v}{\rightarrow}(2)
$

$
\begin{array}{l}
\vec{P}(2)=2[4 \hat{i}+4 \hat{j}], p(2)=8 \hat{i}+8 \hat{j} \mathrm{~kg} . \mathrm{m} / \mathrm{s} \\
\vec{F}=m \underset{a}{\rightarrow}
\end{array}
$

$
\begin{array}{l}
\vec{v}{v}(t)=2 t \hat{i}+t^{2} \hat{j} \\
\vec{a}(t)=\frac{d \rightarrow(t)}{d t}=2 \hat{i}+2 t \hat{j} \\
\vec{F}(2)=2(2 \hat{i}+4 \hat{j})=4 \hat{i}+8 \hat{j} N
\end{array}
$