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  4. The velocity of the particle at any time t is given by v = 2t(3 - t) m s-1. At what time is its velocity maximum ?

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Q. The velocity of the particle at any time $t$ is given by $v = 2t(3 - t) \,m \,s^{-1}$. At what time is its velocity maximum ?

Motion in a Straight Line

Solution:

Given : $v = 2t(3 - t)$ or $v = 6t-2t^2$
$\frac{dv}{dt}=6-4t$ ;
For maximum velocity, $\frac{dv}{dt}=0$
$\therefore 6-4t=0$ or $t=\frac{3}{2}s$