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

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3 s

$\frac{2}{3} s$

$\frac{3}{2} S$

2 s

answer is D.

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Detailed Solution

Given : $v = 2 t (3 - t) or v = 6 t - 2 t^{2}$

$\frac{dv}{dt} = 6 - 4 t$

At maximum velocity, $\frac{dv}{dt} = 0$

$∴ 6 - 4 t = 0 or t = \frac{3}{2} s$

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