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

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Given data: m = 2kg

At t = 2s, $\overrightarrow{v }(2) = 2(2)\widehat{i} + (2)2\widehat{j}$

$\overrightarrow{v} (2) = 4\widehat{i}+ 4\widehat{j}$

Now, momentum $\overrightarrow{P }(2) = m\overrightarrow{v} (2)$

$\overrightarrow{P }(2) = 2[4\widehat{i} + 4\widehat{j}]$

$\overrightarrow{P }(2) = 8\widehat{i} + 8\widehat{j}kg ms^{-1}$

$\overrightarrow{F }(2) = m\overrightarrow{a}$

$\overrightarrow{F }(2) = m\overrightarrow{a}(2)$

$v(t)=2t\widehat{i}+ t^{2}\widehat{j}$

$\overrightarrow{a }(t) = \frac{d\overrightarrow{v}(t)}{dt} = 2\widehat{i} + 2t\widehat{j}$

$\overrightarrow{a }(2) = 2\widehat{i} + 2(2)\widehat{j}$

$= 2\widehat{i} + 4\widehat{j}$

Thus, $\overrightarrow{F} (2)= 2(2\widehat{i} + 4\widehat{j})$

$= 4\widehat{i} + 8\widehat{j}N$

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