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?

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

the one with the highest speed

this is poiselle's equation from fluid mechanic in physics. mech eng