Question

If a stone is dropped from a height of 400 feet, its height after t seconds is given by s = 400 − 16t2. Find its instantaneous velocity function.

Answer 1

`v = -32 t`

Step-by-step explanation:

given,

s = 400- 16 t²

we know,

Velocity of an object is defined as the change in displacement per unit change in time.

velocity an also be return as

`v = (ds)/(dt)`

`v = (d)/(dt)(400-16t^2)`

`v= 0 -2* 16 t`

`v = -32 t`

Hence, instantaneous velocity function given by
`v = -32 t`

To calculate instantaneous velocity, you need to insert value of time.

ex, instantaneous velocity at t = 4 s

v = -32 x 4 = -128 m/s.