In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 9.9 m/s in 2.0 s. Assuming that the player accelerates uniformly, determine the distance he runs.
a = v/t = 9.9/2 = 4.95
s = 1/2 at^2 = 1/2 (4.95)(2^2) = 9.90
To determine the distance that the basketball player runs, you can use the formula for distance traveled during uniformly accelerated motion:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Given:
Initial velocity (u) = 0 m/s (starting from rest)
Final velocity (v) = 9.9 m/s
Time (t) = 2.0 s
First, calculate the acceleration (a) using the formula:
Acceleration (a) = (final velocity - initial velocity) / time
Acceleration = (9.9 m/s - 0 m/s) / 2.0 s = 4.95 m/s²
Next, substitute the values into the distance formula:
Distance = (0 m/s) * (2.0 s) + (1/2) * (4.95 m/s²) * (2.0 s)^2
Distance = 0 + 0.5 * 4.95 * 4.0
Distance = 0 + 9.9
Distance = 9.9 meters
Therefore, the basketball player runs a distance of 9.9 meters.
To determine the distance the basketball player runs, we can use the equation:
distance = initial velocity * time + 0.5 * acceleration * time^2
First, we need to find the acceleration. The player starts from rest, so the initial velocity is 0 m/s. The final velocity is given as 9.9 m/s, and the time taken is 2.0 seconds. Since the player accelerates uniformly, we can find the acceleration using the formula:
acceleration = (final velocity - initial velocity) / time
acceleration = (9.9 m/s - 0 m/s) / 2.0 s
acceleration = 4.95 m/s^2
Now we can substitute the values into the distance formula:
distance = 0 m/s * 2.0 s + 0.5 * 4.95 m/s^2 * (2.0 s)^2
distance = 0 + 0.5 * 4.95 m/s^2 * 4.0 s^2
distance = 0 + 0.5 * 4.95 m/s^2 * 16.0 s^2
distance = 39.6 m
Therefore, the basketball player runs a distance of 39.6 meters.