Question

A runner is at the starting line and hears the starting gun. He starts running from rest with a constant acceleration ai = 0.53 m/s2. He crosses the finish line at d = 100 m and then begins slowing down. It takes him a time interval tr to cross the finish line. It takes him a time interval ts = 7.5 s to return to rest after crossing the finish line. Use the given coordinate system where x is positive to the right. a)Enter an expression for the time, tr, it takes for the runner to cross the finish line, in terms of d and ai

Answer 1

To find the time, tr, it takes for the runner to cross the finish line, we can use one of the kinematic equations that relate displacement, initial velocity, acceleration, and time. Since the runner starts from rest, his initial velocity is zero, so we can use the equation:

Δx=v0​t+21​at2

where Δx is the displacement, v0​ is the initial velocity, a is the acceleration, and t is the time. Plugging in the given values of Δx=d, v0​=0, and a=ai​, we get:

d=0+21​ai​t2

Solving for t, we obtain:

t=ai​2d​​

This is the expression for the time, tr, it takes for the runner to cross the finish line, in terms of d and ai.