How Far Does the Trooper Travel to Catch the Speeder?

[nkallivrousis]

Homework Statement

A state trooper sets up a radar trap. A speeder passes the trooper and continues going at a constant speed of 40 m/s. The instant the speeder passes the trooper, the trooper accelerates at 5.0 m/s/s for 10 seconds and then continues at a constant speed. How far will the trooper travel before she catches up to the speeder?

Homework Equations

d=v1t+1/2at^2
d=1/2at^2

The Attempt at a Solution

I figured out the distance traveled for the first ten seconds by the police man to be 250 meters and his final velocity being 50 m/s. The speeder's distance in 10 seconds is 400 meters. Now I do not know how to find the distance that it takes for the cop to catch the speeder.

 

[CompuChip]

So what is the relative distance between them at the moment the cop stops accelerating?
Then with their relative velocity, how long will it take the cop to cover that distance?

 

[nkallivrousis]

The distance between the two cars would be 150 meters apart. The problem is that I do not know how to find a formula to discover the rest of the distance covered