Question

starting from rest at one set of traffic lights a car accelerates from rest to a velocity of 12m/s. It maintains this speed for 42 seconds until it decelerates to rest at the next set of red lights 60 seconds after leaving the first set. If the acceleration and deceleration are equal find the distance between the two set of lights?

Answer 1

It had 42 seconds at 12/m/s so that's 42(12) = 504
Acceleration and deceleration times were (60-42)/2 = 9s each
a = (12 m/s)/(9s) =4/3
a' = (-12 m/s)(9s) = -4/3

distance = (a/2) t^2 = (4/6)(9s)^2=36 while accelerating
distance = (12)(9) - (a/2) t^2= 72 while decelerating

total distance = 36 + 504 + 72.