Really easy 1-d motion question

[mewmew]

Ok, I have a pretty dumb question. A motorcycle cop starts to accelerate with a constant acceleration, a , at the same time a car goes by with a constant velocity, Vcar, find what time it takes to reach the car, the distence, etc. Now, I figured it out as it was a pretty easy problem but I dont understand why it wont work in relative motion as follows: The cop has an initial velocity of -Vcar and accelerates with his acceleration a untill he reaches a velocity of 0. I put it into 0 = Vo + at but that doesnt give me the right answer, so im sure my logic of relative motion is just wrong and am wondering why? Thanks for any help, im sure I am just not thinking of something super easy.

[freddy]

In order for the cop to catch the car he must accelerate up to the same speed of the car (v = 0) at which point he is no longer losing ground on it. After that point he continues accelerating in order to gain on the car until he reaches it. If you want to do the problem from the other car's refrence frame you'll have to look at when the cop reaches the car's x=0 from an initial velocity of Vo and acceleration of a.

[Tide]

Your mistake is that the motorcycle's speed will be the same as the car's speed when it overtakes the car.