A motorist travelling at 72km/h on a straight road approaches a traffic light which turn red when he is 55m away from the stop line.The reaction time is 0.7s.With the brakes applied fully,the vehicle decelerates at 5m/s^2.How far from the stop line will he stop and on which side of the stop line?
It will take him
T = 72[km/h]/5[m/s²] = 0.7[s] + 72*1000/3600[m/s]/5[m/s²] = 4 s
to come to a complete stop after applying the brakes.
L = (0.7[s] + 4[s]/2)*72*1000/3600[m/s] ≈ 54 m
before coming to a stop. So, he'll stop 55[m] - 54[m] = 1 meter before the stop line.
The path is L = v*t0 + a*t^2/2 where v = 72 kmph is the initial velocity, a = 5 m/s^2 is the deceleration, t is time of decelerated motion and t0 = 0.7 s is a reaction time. We know that a*t = v, thus L = v*t0 + v*t/2 = (t0 + t/2)*v