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.
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.
To estimate Usain Bolt's average acceleration in each interval, we need to use the formula:
Average acceleration = (final velocity - initial velocity) / time
First, let's calculate the time intervals for each interval. Given that the distance covered in each interval is 20m, we can assume the time taken to cover each interval is the same.
Time interval for 0-20m = 20m / 6.38m/s = 3.135s (approximately)
Time interval for 20-40m = 20m / (11.36m/s - 6.38m/s) = 3.297s (approximately)
Time interval for 40-60m = 20m / (12.05m/s - 11.36m/s) = 3.733s (approximately)
Now, let's calculate the average acceleration in each interval.
For the 0-20m interval:
Average acceleration = (6.38m/s - 0m/s) / 3.135s = 2.037 m/s^2 (approximately)
For the 20-40m interval:
Average acceleration = (11.36m/s - 6.38m/s) / 3.297s = 1.509 m/s^2 (approximately)
For the 40-60m interval:
Average acceleration = (12.05m/s - 11.36m/s) / 3.733s = 0.185 m/s^2 (approximately)
Thus, the estimated average accelerations in the 0-20m, 20-40m, and 40-60m intervals are 2.037 m/s^2, 1.509 m/s^2, and 0.185 m/s^2 respectively.
To estimate Usain Bolt's average acceleration in different intervals, we will use the formula:
Average acceleration = (final velocity - initial velocity) / time
Let's calculate the average accelerations for each interval:
1. 0-20m interval:
- Initial velocity = 0 m/s (since it's the start)
- Final velocity = 6.38 m/s
- Time = 20m / 6.38m/s = 3.13 seconds
Average acceleration = (6.38 m/s - 0 m/s) / 3.13 seconds
2. 20-40m interval:
- Initial velocity = 6.38 m/s
- Final velocity = 11.36 m/s
- Time = 20m / (11.36m/s - 6.38m/s) = 3.18 seconds
Average acceleration = (11.36 m/s - 6.38 m/s) / 3.18 seconds
3. 40-60m interval:
- Initial velocity = 11.36 m/s
- Final velocity = 12.05 m/s
- Time = 20m / (12.05m/s - 11.36m/s) = 10 seconds
Average acceleration = (12.05 m/s - 11.36 m/s) / 10 seconds
By performing these calculations, you will find the average accelerations for each interval of 0-20m, 20-40m, and 40-60m in Usain Bolt's sprint at the 2012 London Olympics.