A commuter travels to work along a road with many traffic signals. After stoppin

Question

A commuter travels to work along a road with many traffic signals. After stopping at one red light the commuter accelerates at 2 m/s Just as he passes a speed camera, he notices that the next traffic light has turned red and he must stop, which he does by reversing his acceleration and now decelerating at a constant rate of 2 m/s coming to a stop just at the traffic light. The distance between the two traffic lights is 800 m. A. How does the time he is speeding up compare to the time he is slowing down? O More time speeding up Same More time slowing down You cannot determine from the information given A1. Explain your reasoning B. How much time does he take to get from the first traffic light to the second? seconds C. What was his maximum speed? m/s D. The speed limit on the road is 45 mi/h. If he is going more than about 15 mi/h faster than that, hell get a traffic ticket in the mail. Do you expect him to get one? No Yes It cannot be determined from the information given

Explanation / Answer

A. If we ignore friction, then time taken to speed up and time taken to slow down will be same as equation used will be v= vo+at with variables interchanged for both conditions.

While speeding up, vo= 0 and v= maximum speed a= 2m/s^2

While slowing down , vo= maximum speed , v = 0 , a = -2 m/s^2

In both cases, time = maximum speed/2

But if we consider friction here, then time taken to speed up will be greater than time taken to slow down, as while speeding up friction acts against the motion, but while slowing down, friction helps in slowing down.

For B and C

Commuter will travel equal distances while speeding up and while slowing down

While speeding up d = 400 m

vo = 0

v = maximum speed reached

t = time taken

a= acceleration = 2m/s^2

using v^2 =vo^2 +2ad

v^2 = 0 + 2(2)(400)

v = 40 m/s [ maximum speed reached] ans to part C

Now

v = vo+at

40 = 0 +2t

t = 20s [ time taken to speed up]

Since time taken to speed up = time taken to slow down

Total time taken to go from one signal to other = 2 x 20 s = 40 s [ ans to par B]

D. His maximum speed is 40 m/s = 89.48 miles/hour which is 44.48 miles/hour greater than maximum speed limit. He will get traffic ticket by mail

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