A particle is moving along a line according to $S = 4 t^{3} - 3 t^{2} + 5 t - 1$ where $S$ is measured in meters and $t$ is measured in seconds. Find the velocity and acceleration at time $t$ . What time the acceleration is zero.

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Detailed Solution

Given, $S = 4 t^{3} - 3 t^{2} + 5 t - 1$

velocity, $V = \frac{d s}{d t} = 12 t^{2} - 6 t + 5$

acceleration, $a = \frac{d v}{d t} = 24 t - 6$

acceleration is zero $\Rightarrow 24 t - 6 = 0$

$\Rightarrow t = \frac{6}{24} \Rightarrow t = \frac{1}{4} \sec \Rightarrow∴ at t = \frac{1}{4} \sec,$

acceleration becomes zero

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