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?
1
Expert's answer
2012-09-28T08:58:26-0400
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.
He'll go
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
Nishan
26.08.14, 06:30
why must the t=4s divide 2 ???
Leave a comment
Thank you! Your comments have been successfully added. However, they need to be checked by the moderator before being published.
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
APPROVED BY CLIENTS
"assignmentexpert.com" is professional group of people in Math subjects! They did assignments in very high level of mathematical modelling in the best quality. Thanks a lot
Comments
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
why must the t=4s divide 2 ???
Leave a comment