# A car capable of a constant acceleration of 3.84 m/s2 is stopped at a traffic light.

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A car capable of a constant acceleration of 3.84 m/s2 is stopped at a traffic light. When the light turns green, the car starts from rest with this acceleration. At the very same moment, a truck traveling with constant velocity 10.4 m/s passes the car.

As the car’s velocity increases, it will eventually move faster than the truck and later overtake it. How far from the light will the car catch up with the truck?

When the car catches up the truck, both has traveled the same amount of time (t) and distance (x). Here one can set up the motion equations for both vehicles:

Car: $x=\frac 12 at^2$

Truck: $x=vt$

Only t and x are unknown and with two equations, you can solve for both.
answered Sep 15, 2014 by (21,750 points)