Assume you are driving at the speed limit v0. As you approach an intersection 21.5 m wide, you see the light turn yellow. During your reaction time of 0.690 s, you travel at constant speed as you recognize the warning, decide whether to stop or to go through the intersection, and move your foot to the brake if you must stop. Your car has good brakes and can accelerate at -2.7 m/s2. Before it turns red, the light should stay yellow long enough for you to be able to get to the other side of the intersection without speeding up, if you are too close to the intersection to stop before entering it. (a) Find the required time interval Δty that the light should stay yellow in terms of v0. (b) Evaluate your answer for v0 = 8.00 m/s = 28.8 km/h. (c) For what value of v0 would Δty be minimal? (d) What is the minimum time interval for part (c)?
Assume you are driving at the speed limit v0. As you approach an intersection 21.5 m wide, you see the light turn yellow. During your reaction time of 0.690 s, you travel at constant speed as you recognize the warning, decide whether to stop or to go through the intersection, and move your foot to the brake if you must stop. Your car has good brakes and can accelerate at -2.7 m/s2. Before it turns red, the light should stay yellow long enough for you to be able to get to the other side of the intersection without speeding up, if you are too close to the intersection to stop before entering it.
(a) Find the required time interval Δty that the light should stay yellow in terms of v0.
(b) Evaluate your answer for v0 = 8.00 m/s = 28.8 km/h.
(c) For what value of v0 would Δty be minimal?
(d) What is the minimum time interval for part (c)?
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