If the distance ' $s$ ' metres transversed by a particle in $t$ seconds is given by $s = t^{3} - 3 t^{2}$ , then the velocity of the particle when the acceleration is zero, in metre/sec is

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Solution

The correct option is C -3
$s = t^{3} - 3 t^{2}$

$∴$ Velocity $v = \frac{d s}{d t} = 3 t^{2} - 6 t$

and acceleration $= \frac{d v}{d t} = 6 t - 6 = 0$ (given) $\Rightarrow t = 1$

Hence required velocity $= v ∣_{t = 1} = 3 - 6 = - 3$ m/s

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If the distance 's' metres transversed by a particle in t seconds is given by s=t3−3t2, then the velocity of the particle when the acceleration is zero, in metre/sec is

The correct option is C -3s=t3−3t2∴ Velocity v=dsdt=3t2−6tand acceleration =dvdt=6t−6=0 (given) ⇒t=1Hence required velocity =v∣t=1=3−6=−3 m/s

If the distance ' $s$ ' metres transversed by a particle in $t$ seconds is given by $s = t^{3} - 3 t^{2}$ , then the velocity of the particle when the acceleration is zero, in metre/sec is

The correct option is C -3
$s = t^{3} - 3 t^{2}$

$∴$ Velocity $v = \frac{d s}{d t} = 3 t^{2} - 6 t$

and acceleration $= \frac{d v}{d t} = 6 t - 6 = 0$ (given) $\Rightarrow t = 1$

Hence required velocity $= v ∣_{t = 1} = 3 - 6 = - 3$ m/s