A person driving her car at 35 km/h approaches an intersection just as the traff

Question

A person driving her car at 35 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning to red, and she is 28 m away from the near side of the intersection (see the figure(Figure 1) ).

Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 m wide. Her car's maximum deceleration is -5.8 m/s2, whereas it can accelerate from 45 km/h to 65 km/h in 6.0 s. Ignore the length of her car and her reaction time.

Explanation / Answer

To begin we must first determine the total distance that the pretty lady must travel in order to either succeed or fail in crossing the distance under 2 seconds without the risk of an accident. This is the addition of the distance of the intersection with her distance from the near side of the intersection. This total distance is 43m.

Let us assume that the pretty lady is in a hurry and wishes to cross the intersection. To do this, she must accelerate from her initial point of 35km/h (or 9.72m/s) in order to ensure that she crosses within 2 seconds. Given that lady is driving with speed of 35km/h (or 9.72m/s) and her car is capable of accelerating from 45km/h to 65 Km/h in 6 seconds. Therefore, Her average acceleration from (45km/h)12.5m/s to 18.1m/s (65km/h) in 6 seconds is given by

(18.1m/s - 12.5m/s)/6s =0.93 m/s^2.

Now she has to accelerate from 35km/h (or 9.72m/s) to 18.1m/s (65km/h) in more than 6 seconds.

Lets assume that car takes x seconds to accelerate from 35km/h (or 9.72m/s) to (45km/h)12.5m/s since data has not been provided.

For the first second of acceleration, the lady would have a total speed of (12.5m/s + 0.93m/s) = 13.43m/s, and the distance traveled for the first second is 13.43m. For 2nd second, the total speed would now be (13.43m/s + 0.93m/s) = 14.36m/s, and the distance from this alone without considering the first second is 14.36m. Thus, her total traveled distance in 2 seconds is now 27.79m. This distance covered is short of even reaching the near side of the intersection, which implies that should she choose to continue, there exists the great probability that the pretty lady would enter into a collision accident, which is indeed very unfortunate, and leads us to conclude that it would be very unwise for her to try and cross the intersection with the given state of the motion of her car.

However, given the above calculations it is interesting to note that, even without extensive physical and mathematical investigations, the answer to this problem is easily obtainable with the knowledge of common traffic rules and regulations. The answer that the pretty lady should try to stop instead of pursue in crossing stems naturally from the rule that once the yellow light is seen, all drivers before it must ready for a stop by immediate deceleration. DRIVE SAFE

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