A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t) = bt^2 - ct^3, where b = 3 m/s^2 and c = 0.110 m/s^3.

Question

a) Calculate the average velocity of the car for the time interval t = 0 to t = 10s.

b) Calculate the instantaneous velocity of the car at t = 0, t = 5.0s, and t = 10.0s

c) How long after starting from rest is the car again at rest?

So I solved part A - 19 m/s just plugging t = 10 into the given formula.

I'm not sure how to solve part b, especially since I thought instantaneous velocity at t = 0 should be 0 given that the car starts at rest. However, my book's answer key says that the velocity at this instant is not zero. What am I missing for calculating instantaneous velocity?

Answer 1

You are missing nothing. Taking the derivative of position with respect to time
v=dx/dt= 2bt - 3ct^2, and at t=0, v=0 The answer key is wrong.