# Help!​A car traveling at a constant speed

label Physics
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schedule 1 Day
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A car traveling at a constant speed of 36.4 m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets in a chase after the car with a constant acceleration of 3.96m/s^2.

how long after the trooper starts the chase does he overtake the speeding car?

Oct 4th, 2015

The trooper overtakes the car after the two have covered equal distance.

Distance(Y) = speed(v)*time(t)

speed =acceleration*time

Distance covered by car= 36.4*t(unknown)

Distance covered by trooper=3.96*t^2+?

But the trooper started chasing a second after the car left the billboard,therefore the distance covered by the car is,

36.4*1 =36.4

Therefore,distance covered by car is equal to distance covered by trooper expressed as,

36.4t=3.96t^2+36.4

solving the system of quadratic equation gives

t= 8 second or 1.13 seconds

This is the time it takes for the trooper to overtake the car.

Oct 4th, 2015

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Oct 4th, 2015
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Oct 4th, 2015
Nov 18th, 2017
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