Usain Bolt ran the 2012 Olympic 100-meter race in 9.63 seconds. If he runs at this rate on a road with a speed limit of 25 miles per hour, how will his speed compare to the speed limit? Justify your answer. (25 mi/hr = 40,234 meters/hr)

1 answer

To compare Usain Bolt's speed during his 100-meter race to the speed limit of 25 miles per hour, we first need to calculate his speed during that race.

  1. Calculate Usain Bolt's speed: Usain Bolt completed the 100-meter race in 9.63 seconds.

    Speed (in meters per second) = Distance / Time

    \[ \text{Speed} = \frac{100 \text{ meters}}{9.63 \text{ seconds}} \approx 10.39 \text{ m/s} \]

  2. Convert Usain Bolt's speed to miles per hour: To convert meters per second to miles per hour, we use the conversion factor \(1 \text{ m/s} = 2.23694 \text{ mi/hr}\).

    \[ \text{Speed in mi/hr} = 10.39 \text{ m/s} \times 2.23694 \frac{\text{mi/hr}}{\text{m/s}} \approx 23.31 \text{ mi/hr} \]

  3. Compare to the speed limit: The speed limit is 25 miles per hour.

    Usain Bolt's speed (approximately 23.31 mi/hr) is less than the speed limit of 25 mi/hr.

Conclusion: Usain Bolt's speed of approximately 23.31 miles per hour is below the speed limit of 25 miles per hour. This means he would be within the legal speed limit if he continued to run at that pace on a road.