Assume you are driving at the speed limit v 0 .As you approach an intersection 2

Question

Assume you are driving at the speed limit v0.As you approach an intersection 23.5 mwide, you see the light turn yellow. During your reaction time of0.510 s, you travel at constant speedas you recognize the warning, decide whether to stop or to gothrough the intersection, and move your foot to the brake if youmust stop. Your car has good brakes and can accelerate at-3.1 m/s2. Before it turnsred, the light should stay yellow long enough for you to be able toget to the other side of the intersection without speeding up, ifyou are too close to the intersection to stop before entering it.(Suggestion: You may find it easier to do part (a) afterfirst doing part (b).) (a) Find the required time intervalty that the light should stay yellow interms of v0.

Explanation / Answer

x = distance needed to stop v = speed limit t1 = time needed to acclerate from v to 0 t2 = how long the light should stay yellow (expressed as deltat in the problem)
The time needed to accelerate from the speed limit to a stopis given by: 0 = v + -3.1t t1 = v/(3.1) The distance needed to stop is given by the formula relatinginitial velocity, acceleration and displacement: x = .51v + .5(-3.1)((v/(3.1))^2)
Now, to check how long the light should stay yellow, you seehow long it would take the car to travel the distance of theintersection and the distance of the decision point(the point thatwe solved for earlier where your car could barely stop). 23.5 + .51v + .5(-3.1)((v/(3.1))^2) = v(t2) t2 = (23.5 + .51v + .5(-3.1)((v/(3.1))^2))/v
Watch out for the grouping.

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