If the displacement of a particle at a point | vedclass

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Question

(D) Given the displacement function $s = 3t^{2} - 12t + 14$. Velocity $v$ is the rate of change of displacement with respect to time $t$, given by $v

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) Given the displacement function $s = 3t^{2} - 12t + 14$. Velocity $v$ is the rate of change of displacement with respect to time $t$, given by $v = \frac{ds}{dt}$. $v = \frac{d}{dt}(3t^{2} - 12t + 14) = 6t - 12$. When the velocity becomes zero, we set $v = 0$: $6t - 12 = 0 \implies 6t = 12 \implies t = 2 	ext{ seconds}$. Now, substitute $t = 2$ into the displacement equation to find the displacement at that instant: $s = 3(2)^{2} - 12(2) + 14$ $s = 3(4) - 24 + 14$ $s = 12 - 24 + 14 = 2 	ext{ units}$. Thus, the displacement of the particle when its velocity is zero is $2 	ext{ units}$.

If the displacement of a particle at a point is given by $s = 3t^{2} - 12t + 14$, then the displacement of the particle when its velocity becomes zero is (in $\text{ units}$)

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