A car traveling at a constant speed of 50.0 m/s passes a trooper on a motorcycle

Question

A car traveling at a constant speed of 50.0 m/s passes a trooper on a motorcycle hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch the car, accelerating at a constant rate of 2.00 m/s2. How long does it take her to overtake the car? Solve this problem by a graphical method. On the same graph plot position versus time for the car and the police officer. (Do this on paper. Your instructor may ask you to turn in this work.)

From the intersection of the two curves read the time at which the trooper overtakes the car.

Explanation / Answer

here,

speed of the car , uc = 50 m/s

accelration of trooper , a = 2 m/s^2

let the time taken by the tropper to approach the car be t

distance travelled by the car = distance travelled by the trooper

uc * (t + 1) = 0 * t + 0.5 * a * t^2

50 * (t + 1) = 0 * t + 0.5 * 2 * t^2

t = 50.98 s

it takes 50.98 s to overtake the car

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