Question

The position of an object at time t is given by s(t) = -9 - 5t. Find the instantaneous velocity at t = 4 by finding the derivative.

Answer 1

`\bf s(t)=-9-5y\implies \left. \stackrel{v(t)}{\cfrac{ds}{dt}=-5} \right|_(t=4)\implies -5`

since the derivative is a constant, it doesn't quite matter what "t" may be.

Answer 2

Instantaneous Velocity is
`-5`

Explanation:

Velocity refers to the speed along with direction or we can say velocity refers to rate of change of position of an object with respect to time.

Let
`s\left ( t \right )` be the position of object . Then the instantaneous velocity is given by
`v\left ( t \right )=s'\left ( t \right )` . At time
`t=t_0` , velocity is given by
`v\left ( t_0 \right )=s'\left ( t_0 \right )`

Given:
`s\left ( t \right )=-9-5t`

On differentiating with respect to time t , we get :

`v\left ( t \right )=s'\left ( t \right )=-5`

At
`t=t_0=4` ,

`v\left ( 4 \right )=s'\left ( 4 \right )=-5`