Question

A car is stopped at a set of traffic lights. It takes off, accelerating at 4.5m/s2 until it is travelling at 60km/h. It maintains this velocity for 3 minutes before braking to a halt over 60m at another set of traffic lights. How far has the car travelled in this trip and how long did the trip take? Plot a velocity vs time graph for this situation.

Answer 1

V = 60km/h = 60000m/3600s = 16.7 m/s.

a = (V-Vo)/t = 4.5 m/s^2
(16.7-0)/t = 4.5
t = 16.7/4.5 = 3.70 s.

d1 = 0.5a*t^2 = 2.25*3.7^2 = 31 m.

d2 = V*t = 16.7m/s * 180s = 3,000 m.

d3 = 60 m.

d1+d2+d3 = 30.8 + 3000 + 60 = 3091 m. =
Total distance traveled.

V^2 = Vo^2 + 2a*d
a = (V^2-Vo^2)/2d =(0-16.7^2)/120=-2.32m/s^2.

V = Vo - 2.32t = 0
16.7 - 2.32t = 0
2.32t = 16.7
t = 7.2 s. To stop.

T = 3.70 + 180 + 7.2 = 190.9 s. = Total
travel time.