The displacement $s$ of a moving particle at time $t$ is given by $s = 5 + 20 t - 2 t^{2}$ . Find its acceleration when the velocity is zero.

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Solution

Given, $s = 5 + 20 t - 2 t^{2}$

Velocity $(v)$ $= \frac{d s}{d t} = 20 - 4 t$

Now, $v = 0$

$∴ 20 - 4 t = 0$

$∴ t = 5$

And acceleration $(a) = \frac{d v}{d t} = - 4$

$∴ {(\frac{d v}{d t})}_{t = 5} = - 4$

Hence, the acceleration is $- 4$ unit/sec $^{2}$ .

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The displacement s of a moving particle at time t is given by s=5+20t−2t2. Find its acceleration when the velocity is zero.

Given, s=5+20t−2t2Velocity (v) =dsdt=20−4tNow, v=0∴20−4t=0∴t=5And acceleration (a)=dvdt=−4∴(dvdt)t=5=−4Hence, the acceleration is −4 unit/sec 2.

The displacement $s$ of a moving particle at time $t$ is given by $s = 5 + 20 t - 2 t^{2}$ . Find its acceleration when the velocity is zero.

Given, $s = 5 + 20 t - 2 t^{2}$

Velocity $(v)$ $= \frac{d s}{d t} = 20 - 4 t$

Now, $v = 0$

$∴ 20 - 4 t = 0$

$∴ t = 5$

And acceleration $(a) = \frac{d v}{d t} = - 4$

$∴ {(\frac{d v}{d t})}_{t = 5} = - 4$

Hence, the acceleration is $- 4$ unit/sec $^{2}$ .