Average Velocity & Instantaneous Velocity...5

Calculus 1
Extra question not from Chapter 1.

Given the position function s(t) = 2t^3 - 2t^2, where s is in meters and t in seconds, find

A. Average Velocity from t = 1 to t = 3
B. Instantaneous Velocity at t = 4

Part A

2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

2(1)^3 - 2(1)^2 = 2(1) - 2(1) = 2 - 2 = 0

Let A_v = average velocity

A_v = (36 - 0)/(2 - 1)

A_v = 36/1 = 36

A_v = 36 m/t

Part B

Let s'(t) = instantaneous velocity

s'(t) = 6t^2 - 4t

Let t = 4

s'(1) = 6(4)^2 - 4(4)

s'(1) = 6(4) - 4

s'(1) = 24 - 16

s'(1) = 8 m/t

You say?

 

correct

 

Very good. This is it for today. My weekend is almost over. It's insane how quickly Saturday and Sunday go by.