Question

The displacement of a body at any time t after starting is given by s= 15t-0.4t^2 . The velocity of the body will be 7m/s after time?

Answer 1

If the answer is 10 seconds here's the method

Answer 2

After 10 seconds velocity of the body will be 7 m/s

Given :

The displacement of a body at any time t after starting is given by s = 15t - 0.4t²

To find :

The time after which velocity of the body will be 7 m/s

Solution :

Step 1 of 2 :

Find velocity of the body at any time t

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

s = 15t - 0.4t²

Differentiating both sides with respect to t we get

$\displaystyle \sf{ \frac{ds}{dt} = (15 \times 1) - (0.4 \times 2t) }$

$\displaystyle \sf{ \implies v = 15 - 0.8t}$

So velocity of the body at any time t is (15 - 0.8t) m/s

Step 2 of 2 :

Find the required time

Let after t seconds velocity of the body will be 7 m/s

By the given condition

$\displaystyle \sf{ 15 - 0.8t = 7 }$

$\displaystyle \sf{ \implies - 0.8t = 7 - 15}$

$\displaystyle \sf{ \implies - 0.8t = - 8}$

$\displaystyle \sf{ \implies 0.8t = 8}$

$\displaystyle \sf{ \implies t = \frac{8}{0.8} }$

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

Hence after 10 seconds velocity of the body will be 7 m/s

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