A certain traffic light is yellow for 2.70 s before it turns red. As you approac

Question

A certain traffic light is yellow for 2.70 s before it turns red. As you approach the intersection, you must decide whether you can safely go through the yellow light before it turns red or whether you have time to stop before reaching the intersection. Suppose your reaction time is 0.455 s, you are initially moving at 20.4 m/s, and you can decelerate at a maximum rate of 4.95 m/s2 when you step on the brakes and accelerate at a maximum rate of 2.82 m/s2 when you step on the gas.

(a) To come to a complete stop before reaching the intersection, what is the minimum distance you can be from the light when it turns yellow?


(b) To pass the light before it turns red, what is the maximum distance you can be from the light when it turns yellow?


(c) Repeat the calculations for parts (a) and (b) for an initial speed of 36.9 m/s, and find the range of distances for which you can neither stop nor get through the light in time.


minimum distance from the light _______________

maximum distance from the light _____________

Explanation / Answer

a)deceleration a1 = 4.95 v^2 - u^2 = -2*a1*s v=0 u=20.4 m/s s= 42.04 m b)traffic light stays yellow for 2.70 s reaction time = 0.455 s so we have 2.70 - 0.455 s before the light turns red hence t= 2.245 s acceleration a2 = 2.82 s=ut + 1/2a2t^2 = 20.4*2.245 + 0.5*2.82*2.245^2 = 52.90 m c)deceleration a1 = 4.95 v^2 - u^2 = -2*a1*s v=0 u=36.9 m/s s= 137.54 m traffic light stays yellow for 2.70 s reaction time = 0.455 s so we have 2.70 - 0.455 s before the light turns red hence t= 2.245 s acceleration a2 = 2.82 s=ut + 1/2a2t^2 = 36.9*2.245 + 0.5*2.82*2.245^2 = 89.95 m minimum distance from the light 89.95 m maximum distance from the light 137.54 m

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