69. I A car starts from rest at a stop sign. It accelerates at 2.0 m/s²

for 6.0 seconds, coasts for 2.0 s, and then slows down at a rate

of 1.5 m/s2 for the next stop sign. How far apart are the stop

signs?

Answer: 108 m

Explanation: First the car start to move from the rest so the distance is equal to d1=a*t^2/2 = 36 m

Second, the car coast fro 2 s, it means that ir moves a constant speed

this speed is obtained from:

v=a*t = 12 m/s under this stage the d2 = v * 2s = 24 m

Third the car start to stop at 1.5 m/s^2

d3 = v*t-a*t^2/2 = 48 m

so the distance between signs is d1+d2+d3 = 36 m + 24 m + 48 m = 108 m