Question
In the 2012 london olympics, usain bolt posted the folllowing speeds in the 100m sprint: 6.38m/s at 20m, 11.36m/s at 40m, and 12.05m/s at 60m. Estimates his average acceleration in the 0-20m, 20-40m, and 40-60m intervals.
Answers
GPT 3.5
To estimate Usain Bolt's average acceleration in the 0-20m interval, we can use the formula for average acceleration:
Acceleration = (Final Velocity - Initial Velocity) / Time Taken
In this case, the final velocity is 6.38 m/s, the initial velocity is 0 m/s (as he starts from rest), and the time taken is 20m / 6.38 m/s = 3.13 seconds.
Acceleration (0-20m) = (6.38 m/s - 0 m/s) / 3.13 s ≈ 2.04 m/s²
Similarly, to estimate his average acceleration in the 20-40m interval, we use the same formula:
Acceleration (20-40m) = (11.36 m/s - 6.38 m/s) / (40m - 20m) ≈ 0.254 m/s²
Finally, for the 40-60m interval, we repeat the process:
Acceleration (40-60m) = (12.05 m/s - 11.36 m/s) / (60m - 40m) ≈ 0.077 m/s²
Therefore, Usain Bolt's average acceleration is approximately:
- 2.04 m/s² in the 0-20m interval,
- 0.254 m/s² in the 20-40m interval, and
- 0.077 m/s² in the 40-60m interval.
Acceleration = (Final Velocity - Initial Velocity) / Time Taken
In this case, the final velocity is 6.38 m/s, the initial velocity is 0 m/s (as he starts from rest), and the time taken is 20m / 6.38 m/s = 3.13 seconds.
Acceleration (0-20m) = (6.38 m/s - 0 m/s) / 3.13 s ≈ 2.04 m/s²
Similarly, to estimate his average acceleration in the 20-40m interval, we use the same formula:
Acceleration (20-40m) = (11.36 m/s - 6.38 m/s) / (40m - 20m) ≈ 0.254 m/s²
Finally, for the 40-60m interval, we repeat the process:
Acceleration (40-60m) = (12.05 m/s - 11.36 m/s) / (60m - 40m) ≈ 0.077 m/s²
Therefore, Usain Bolt's average acceleration is approximately:
- 2.04 m/s² in the 0-20m interval,
- 0.254 m/s² in the 20-40m interval, and
- 0.077 m/s² in the 40-60m interval.