To find the distance traveled and the acceleration of the bicyclist, we can use the following steps:
1. Convert the initial and final velocities from mph to ft/s:
- The initial velocity is 0 mph, which is 0 ft/s.
- The final velocity is 30.0 mph, which is 44 ft/s (1 mph = 1.47 ft/s).
2. Use the formula for distance traveled during constant acceleration:
- The formula is: distance = (initial velocity * time) + (0.5 * acceleration * time^2).
- Since the initial velocity is 0, the formula simplifies to: distance = 0.5 * acceleration * time^2.
3. Rearrange the formula to solve for distance:
- distance = 0.5 * acceleration * time^2.
4. Substitute the given values into the formula:
- The time is 5.30 s.
- The final velocity is 44 ft/s.
- Rearranging the formula, we get: distance = 0.5 * acceleration * (5.30 s)^2.
5. Solve for distance:
- Substitute the values into the formula and calculate the distance:
distance = 0.5 * acceleration * (5.30 s)^2.
6. Calculate the acceleration:
- Rearrange the formula to solve for acceleration:
acceleration = (2 * distance) / (time^2).
7. Substitute the known values into the formula and calculate the acceleration:
- acceleration = (2 * distance) / (5.30 s)^2.
By following these steps, you can find the distance traveled (in ft) and the acceleration (in ft/s²) of the bicyclist.
I hope this explanation clarifies how to calculate the distance traveled and the acceleration. Let me know if you have any further questions!