Question 264770: At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.80 m/s^2. At the same instant, a truck, traveling with a constant speed of 14.7 m/s, overtakes and passes the automobile.
How far beyond its starting point does the automobile overtake the truck?
How fast is the automobile traveling when it overtakes the truck?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 2.80 m/s^2. At the same instant, a truck, traveling with a constant speed of 14.7 m/s, overtakes and passes the automobile.
How far beyond its starting point does the automobile overtake the truck?
How fast is the automobile traveling when it overtakes the truck?
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For the car, s = (at^2)/2 = 3.92t^2
For the truck, s = 14.7t
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When the distances are equal 14.7t = 3.92t^2
3.92t^t - 14.7t = 0
t = 0 (at the light)
t = 14.7/3.92 = 3.75 seconds
At 3.75 seconds, the auto catches up to the truck.
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s = 14.7*3.75 = 55.125 meters from the light.
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Auto speed = 3.92*3.75 = 14.7 m/sec when it overtakes the truck
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