a runner moving at a speed of 5.60 m/s rounds a curved track with a 60.0 m radius. what is the runners acceleration?
V^2/R
To find the runner's acceleration, we can use the formula for centripetal acceleration:
acceleration = (velocity^2) / radius
Here's how you can calculate it step by step:
Step 1: Determine the values given in the problem:
- Runner's speed (velocity) = 5.60 m/s
- Radius of the curved track = 60.0 m
Step 2: Plug in the values into the formula:
acceleration = (5.60 m/s)^2 / 60.0 m
Step 3: Calculate the numerator of the equation:
(5.60 m/s)^2 = 31.36 m^2/s^2
Step 4: Divide the numerator by the radius to get the acceleration:
acceleration = 31.36 m^2/s^2 / 60.0 m
Step 5: Simplify the equation:
acceleration = 0.5227 m/s^2
Therefore, the runner's acceleration is approximately 0.5227 m/s^2. This means the runner's velocity is changing by 0.5227 meters per second every second.