A truck is stopped at a stoplight. When the light turns green, the truck accelerates at 2.5 meters per second squared. At the same instant, a car passes the truck going 15 meters per second. Where and when does the truck catch up with the car?

Question

A truck is stopped at a stoplight.  When the light turns green, the truck accelerates at 2.5 meters per second squared.  At the same instant, a car passes the truck going 15 meters per second.  Where and when does the truck catch up with the car?

drwls · Answer

car's distance travelled X1 = 15 t
truck's distance travelled X2 = (1/2)2.5 t^2 = 1.25 t^2
Set X1 =X2 and solve for t. We are looking for the solution that is not t=0.
1.25 t^2 = 15 t
t^2 - 12 t = 0
t (t-12) = 0