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At the instant the traffic light turns green, a car that has been waiting at the...

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted August 21, 2013 at 10:30 AM via web

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At the instant the traffic light turns green, a car that has been waiting at the intersection starts ahead with a constant acceleration of 3.20 m/s^2. At the same instant a truck, travelling with a constant speed of 20.0m/s, overtakes and passes the car. How far beyond its starting point, in metres, does the car overtake the truck?

Please explain your answer and formula used.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 21, 2013 at 10:46 AM (Answer #1)

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When the traffic light turns green, a car that has been waiting at the intersection starts with a constant acceleration of 3.2 m/s^2. At the same instant it is overtaken by a truck moving at a constant speed of 20 m/s.

Let the distance covered before the car overtakes the truck be D. The time taken by the truck to travel D m is given by the formula T = D/V where D is the distance traveled by the truck in time T moving at V m/s.

T = D/20

The distance traveled by an object in t seconds, if the initial speed is u and the acceleration a is given by d = u*t + (1/2)*a*t^2.

For the car, u = 0 m/s and a = 3.2 m/s^2. The car travels a distance D in time D/20. Substituting these values in the formula provided earlier gives:

`D = 0 + (1/2)*3.2*(D/20)^2`

=> 800D = 3.2D^2

=> D = 250

The car overtakes the truck after 250 meters.

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