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Differentiation

The velocity ...

Question

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

2 s

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3 s

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\frac{2}{3} s

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\frac{3}{2} s

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Solution

The correct option is D $\frac{3}{2} s$
Given: $v = 2 t (3 - t) o r v = 6 t - 2 t^{2}$
$\frac{d v}{d t} = 6 - 4 t$
At maximum velocity, $\frac{d v}{d t} = 0$
$∴ 6 - 4 t = 0$ or $t = \frac{3}{2} s$

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