Solve the given problem:
Problem: Two horses leave the starting the beginning of a 2000 m long race. The brown horse gate at has an acceleration of 2.2 m/s and a top constant speed of 18 m/s. The black horse has an acceleration of 1.7 m/s2 and a top constant speed of 20 m/s. which horse wins the race? Assume that each horse's top is what it can sustain for the rest of the race after the initial constant speed acceleration period.
I known the correct answer but I need to know how to get that. Thanks in advance!