The position of a particle is given by $s = t^{3} - 6 t^{2} - 15 t$ where $s$ in metres, $t$ is in seconds. If the particle is at rest, then time $t = . . . . .$

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Solution

The correct option is A $5$
$S = t^{3} - 6 t^{3} - 15 t$
Velocity of the particle $V = \frac{d s}{d t}$
$∴ V = 3 t^{2} - 12 t - 5$
Particle is at rest
$∴ 3 t^{2} - 12 t - 15 = 0$
$∴ t^{2} - 4 t - 5 = 0$
$∴ t^{2} - 5 t + t - 5 = 0$
$∴ t (t - 5) + 1 (t - 1) = 0$
$∴ (t - 5) (t + 1) = 0$
$∴ t = 5; t = - 1$

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The position of a particle is given by s=t3−6t2−15t where s in metres, t is in seconds. If the particle is at rest, then time t=.....

The correct option is A 5S=t3−6t3−15tVelocity of the particle V=dsdt∴V=3t2−12t−5Particle is at rest∴3t2−12t−15=0∴t2−4t−5=0∴t2−5t+t−5=0∴t(t−5)+1(t−1)=0∴(t−5)(t+1)=0∴t=5;t=−1

The position of a particle is given by $s = t^{3} - 6 t^{2} - 15 t$ where $s$ in metres, $t$ is in seconds. If the particle is at rest, then time $t = . . . . .$