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  4. A body is acted on by a force given by F=(15+3 t2) N. The impulse received by the body during the first 2 seconds is

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Q. A body is acted on by a force given by $F=\left(15+3 t^{2}\right) N$. The impulse received by the body during the first $2$ seconds is

AP EAMCETAP EAMCET 2019

Solution:

Given,
Force, $F=\left(15+3 t^{2}\right) N$
$\therefore $ Impulse, $ I=\int\limits_{0}^{t} F \cdot d t=\int\limits_{0}^{t}\left(15+3 t^{2}\right) d t $
For, $t=2 \,s $
$I =\left[15 t+3 \times \frac{t^{3}}{3}\right]_{0}^{2} $
$I=15 \times 2+(2)^{3}=30+8=38 \,Ns$