consider the position function...

Question

Consider the position function s(t)=-4.9 t^2 + 27 t + 23. Complete the following table with the appropriate average velocities and then make a conjecture about the value of the instantaneous velocity at t equals 4.

intervals:
[4,5]
[4,4.1]
[4,4.01]
[4,4.001]
[4,4.0001]

Thanks for any help!

Answer 1

s(t) is the position function

 

To find the average velocity you have to find the change in position and divide by the change in time

 

The first interval is 1 second [4,5]

 

s(5) = 115

s(4) = 52.6

 

Δs = 115-52.6 = 62.4

Since Δt = 1, the velocity at this interval is 62.4 

 

Repeat for the rest of the intervals