Yes, the time it takes to run a 100-meter race is indeed a function of the speed at which you run. In mathematical terms, speed is defined as the distance traveled divided by the time taken. This can be expressed in the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Rearranging this formula to solve for time gives us:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In the context of a 100-meter race, the distance is constant at 100 meters. Therefore, the time it takes to complete the race can be expressed as:
\[ \text{Time} = \frac{100 , \text{meters}}{\text{Speed}} \]
From this equation, it is clear that if you increase your speed, the time required to complete the race decreases, and conversely, if you decrease your speed, the time increases. This indicates a functional relationship where time is dependent on speed, and we can describe it as a function:
- Input: Speed
- Output: Time taken to complete the race
This relationship defines a hyperbolic function, demonstrating that time is inversely proportional to speed for a fixed distance.
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