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?
