An Olympic runner is at the starting gate and hears the starting gun. He begins running with a constant acceleration ai = 0.55 m/s2. He crosses the finish line at d = 100 m and then begins slowing down. It takes him tr to cross the finish line. It takes him ts = 7.5 s to return to rest after crossing the finish line.
1. Find an expression for the time it takes for the runner to cross the finish line, tr, from the start in terms of d and ai.
2. Using only acceleration, ai, and time, tr, write an expression for the runner's final speed, vr, when he crosses the finish line.