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  4. Speed of a particle moving in a straight line varies with time as v = (3 + 2t) m/s. The distance covered in first 3 second is

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Q. Speed of a particle moving in a straight line varies with time as $v = (3 + 2t) \,m/s$. The distance covered in first $3$ second is

Solution:

$v = 3+ 2t$
$ dx= vdt$
$dx = \left(3+ 2t\right)dt$
$\int dx = \int\left(3+2t\right)dt$
$ x_{f} -x_{i} = \left[3t+\frac{2t^{2}}{2}\right]_{0}^{3} $
$s = \left(3\times3 +3^{2}\right)-0 $
$ s= 18\, m$