Missing parts in the text of the exercise:
- The distance from the traffic light is given by

, where

and

Solution:
part a) <span>calculate the average velocity of the car for the time interval t=0 to t=8.0 s
- The average velocity is given by the ratio between the distance covered in the time interval:
</span>

x(0 s), the distance covered after t=0 s, is zero, while the distance after t=8.0 s is


Therefore, the average velocity is

part b) <span>calculate the instantaneous velocity of the car at t=0, t=4.0 s and t=8.0 s
- The instantaneous velocity can be found by performing the derivation of x(t):
</span>

<span>So now we just have to substitute t=0, t=4 s and t=8 s:
- t=0: v(0)=0
- t=4 s: </span>

- t=8 s:

part c) <span>how long after starting from rest is the car again at rest?
- To solve this part we must find the value of t for which v(t)=0, so:
</span>


<span>The first solution is t=0 s, which corresponds to the beginning of the motion, so we are not interested in this value. The second solution is
</span>

<span>and this is the time at which the car is at rest again.</span>