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Q.
If acceleration of a panicle at any time is given by $a=2 t+5$ Calculate the velocity after $5 \,s$, if it starts from rest.
Haryana PMTHaryana PMT 2007Motion in a Straight Line
Solution:
$a=2 t+5$
or $\frac{d v}{d t}=2 t+5$
or $d v=(2 t+5) d t$ ... (i)
Integrating Eq. (i) on both sides within the limits
$\int\limits_{0}^{v} d v=\int\limits_{0}^{5}(2 t+5) d t$
or $v=\left[\frac{2 t^{2}}{2}+5 t\right]_{0}^{5}$
$=[5 \times 5+5 \times 5]=50 \,m / s$