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Unformatted text preview: Ph1a Quiz #1 Solutions Robert Forster, Fall 2005 Problem 1 (5 points) - Traffic Light Troubles A motorist is approaching a green traffic light at constant velocity v when, at t = 0, the light turns yellow. The car is currently a distance d from the intersection, the drivers reaction time is , and the safe braking acceleration of the car is a . (a) (1 point) What is the minimum distance from the intersection d min that will allow the driver to react to the yellow light and still have time to safely stop the car? First, the driver must react to the yellow light. During this time he travels at a constant velocity, v : d react = v (1) Once the driver recognizes the light, he applies the brakes until the car stops. t brake = v /a (2) d brake = v t brake- 1 2 at 2 brake (3) = v 2 a- 1 2 v 2 a (4) = 1 2 v 2 a (5) The closest distance to the light the car can be and still stop in time is the sum of these two distances: d min = v + 1 2 v 2 a (6) (b) (1 point) Suppose the motorist wishes to beat the light. If the light remains yellow for a time t Y before turning red, what is the maximum distance from the intersection d max that will allow the car to just enter the intersection by the time the light turns red? (Assume the car continues at a constant velocity v .) If the driver wants to make it through the intersection without stopping, slowing down, or speeding up, the maximum distance he can be from the light is the distance he covers in the time the light is yellow: d max = v Y (7) (c) (2 points) If the drivers speed v is faster than a critial speed v c , there will be a range of distances d such that the car can neither safely stop in time nor continue through the intersection without running the light (ie.continue through the intersection without running the light (ie....
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