Question

the displacement of a body at any time t after starting is given by s = 10t - 0.1t 2 . After how much time the velocity of the body becomes zero.

Answer 1

After 50 seconds the velocity of the body becomes zero.

Given :

The displacement of a body at any time t after starting is given by s = 10t - 0.1t²

To find :

The time after which velocity of the body becomes zero.

Solution :

Step 1 of 3 :

Write down displacement of the body at any time t

Here it is given that displacement of a body at any time t after starting is given by

s = 10t - 0.1t²

Step 2 of 3 :

Find velocity of the body at any time t

$\displaystyle \sf{ s = 10t - 0.1 {t}^{2} }$

Differentiating both sides with respect to t we get

$\displaystyle \sf{ \frac{ds}{dt} = 10 - 0.1 \times 2t }$

$\displaystyle \sf{ \implies \: v = \frac{ds}{dt} = 10 - 0.2t }$

So velocity of the body at any time t is 10 - 0.2t

Step 3 of 3 :

Find the time after which velocity of the body becomes zero.

Let after t seconds after which velocity of the body becomes zero.

∴ v = 0

$\displaystyle \sf{ \implies 10 - 0.2t = 0}$

$\displaystyle \sf{ \implies - 0.2t = - 10}$

$\displaystyle \sf{ \implies 0.2t = 10}$

$\displaystyle \sf{ \implies t = \frac{10}{0.2} }$

$\displaystyle \sf{ \implies t = 50}$

Hence after 50 seconds the velocity of the body becomes zero.

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Answer 2

Given:        $s = 10t - 0.1t^{2}$

Now, differentiating the equation w.r.t t,

                     $\frac{ds}{dt} = 10 - 0.2t$

                 ∵  $v = \frac{ds}{dt}$

          $v = 10 - 0.2t$

Suppose the velocity becomes zero after time t,

            $0 = 10 - 0.2t$

              $t = \frac{10}{0.2}$

              $t = 50 seconds$

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