Help!‚ÄčA car traveling at a constant speed

Physics
Tutor: None Selected Time limit: 1 Day

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

Thank you for the opportunity to help you with your question!

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.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 4th, 2015

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