Where do two bodies meet?

A car starts from rest at a signal and speeds up at $2\ \text{m/s}^2$. At the same moment, a cyclist $50\ \text{m}$ ahead rides on at a steady $6\ \text{m/s}$. When does the car catch the cyclist? You will make the program find out by stepping through time, then check it with algebra.

The idea. They meet when their positions are equal:

Your tasks.

1. Make the two functions return the car's and the cyclist's positions.
2. Find where they meet, from the meeting time the loop finds.
3. Solve $t^2 - 6t - 50 = 0$ for the exact meeting time.