In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 8.49 m/s in 1.89 s. Assuming that the player accelerates uniformly, determine the distance he runs.

vf=vi+at solve for a

To determine the distance the basketball player runs, we need to use the kinematic equation that relates distance (d), initial velocity (u), final velocity (v), and time (t) for uniformly accelerated motion:

d = ut + (1/2)at^2

Where:
d = distance
u = initial velocity
v = final velocity
t = time
a = acceleration

First, let's find the acceleration of the basketball player. Since the player starts from rest (u = 0), we can use the following equation:

v = u + at

8.49 m/s = 0 + a * 1.89 s

Solving for a, we get:

a = (8.49 m/s) / (1.89 s)
a ≈ 4.49 m/s^2

Now that we know the acceleration, we can use it to find the distance using the equation:

d = ut + (1/2)at^2

Plugging in the values:

d = (0 m/s)(1.89 s) + (1/2)(4.49 m/s^2)(1.89 s)^2

Calculating:

d = 0 + (1/2)(4.49 m/s^2)(3.5721 s^2)
d = (1/2)(20.146429 m)
d ≈ 10.07 m

Therefore, the basketball player runs approximately 10.07 meters.