Question

The height, h , in meters of a dropped object after t seconds can be represented by h ( t ) = − 4.9 t 2 + 136 . What is the instantaneous velocity of the object one second after it is dropped?

Answer 1

Answer:

The velocity of the object 1 s after it is dropped is -9.8 m/s.

Explanation:

Hi there!

The instantaneous velocity is defined by the change in height over a very small time. Mathematically, it is expressed as the derivative of the function h(t):

instantaneous velocity = dh/dt

dh/dt = h´(t) = -2 · 4.9 · t

h´(t) = -9.8 · t

Now we have to eveluate the function h´(t) at t = 1 s:

h´(1) = -9.8 · (1) = -9.8

The velocity of the object 1 s after it is dropped is -9.8 m/s.