To determine how Usain Bolt's speed compares to the speed limit, we first need to calculate his speed in meters per second during the 2012 Olympic 100-meter race.
Usain Bolt completed the 100 meters in 9.63 seconds. We can calculate his speed as follows:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{100 \text{ meters}}{9.63 \text{ seconds}} \approx 10.39 \text{ meters/second} \]
Next, we need to compare this speed to the speed limit, which is given in miles per hour. First, we will convert Bolt's speed from meters per second to miles per hour. We can use the following conversion factors:
1 mile = 1609.34 meters
1 hour = 3600 seconds
Using these, we convert Usain Bolt's speed:
\[ \text{Speed in miles per hour} = \text{Speed in meters/second} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} \times \frac{1 \text{ mile}}{1609.34 \text{ meters}} \]
Substituting Bolt’s speed into this formula:
\[ \text{Speed in miles per hour} = 10.39 \text{ meters/second} \times \frac{3600}{1} \times \frac{1}{1609.34} \]
Calculating this step-by-step:
- Calculate \(10.39 \times 3600\):
\[ 10.39 \times 3600 \approx 37404 \text{ meters/hour} \]
- Now convert this to miles per hour:
\[ \text{Speed in miles per hour} \approx \frac{37404}{1609.34} \approx 23.2 \text{ miles/hour} \]
Now we have Usain Bolt's speed of approximately 23.2 miles per hour.
Finally, we compare this with the speed limit of 25 miles per hour:
- Usain Bolt's speed: 23.2 miles/hour
- Speed limit: 25 miles/hour
Conclusion:
Usain Bolt's speed of approximately 23.2 miles per hour is lower than the speed limit of 25 miles per hour. Therefore, if he continues to run at his Olympic 100-meter race speed, he would be within the speed limit, but not exceed it.