# An interesting case for a race

**Classical Mechanics**Level 2

In a car race, car \(A\) takes \(t=5\) seconds less than car \(B\) to finish, and passes the finishing point with a speed \(v\) m/s faster than car \(B.\)

Assume that both cars and \(A\) and \(B\) start from rest, and travel with constant accelerations of \(\displaystyle a_1=9\text{ m/s}^2\) and \(\displaystyle a_2=4\text{ m/s}^2,\) respectively.

Find \(v.\)