In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 5.45 m/s in 3.02 s. Assuming that the player accelerates uniformly, determine the distance he runs.

Recall that average velocity v is given by

v = ∆x/∆t

where ∆x is displacement and ∆t is time.

Under constant acceleration, average velocity is also equal to the average of the initial and final velocities,

v = (v₂ + v₁)/2

The player starts at rest, so v₁ = 0, and speeds up to v₂ = 5.45 m/s in a matter of ∆t = 3.02 s. So

∆x = (v₂ + v₁) ∆t / 2

∆x = (5.45 m/s) * (3.02 s) / 2

∆x ≈ 8.23 m

wavelength divides in half and speed stays the same.