Question

A 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 = 6.5 s to return to rest after crossing the finish line. For this problem, use a coordinate system with the runner is moving in the positive direction.

Randomized Variables
ai = 0.55 m/s2
ts = 6.5 s
show answer No Attempt 33% Part (a) 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.

Answer 1

during the run:
vf^2=vi^2 + 2ad solve for vf

but vf= ai*t solve for time t.
so sqrt (2ad)=ai*t
square both side
2ad=a^2 t^2
t= sqrt (2d/a)