Two particles move in opposite directions around a circular track. The first moves at a constant speed of $\text{10 m/s.}$ The speed of the second increases at a constant rate of $\text{2 m/s}$ every second. The particles are at the same position $\text{A}$ at time $0,$ with the second particle being momentarily at rest at $t=0$. We are told that the second meeting of these particles after time $0$ takes place at the point $\text{A}$. We assume that the particles magically cross each other the first time they meet with no change in their instantaneous velocities. Given this information:
- What is the circumference of the track?
- At what time did the particles meet for the first time after time $0?$
