Question

The world record for the hundred meter dash is \(9.58 \mathrm{~s}\). What is the corresponding average speed in units of \(\mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h}, \mathrm{ft} / \mathrm{s}\), and \(\mathrm{mi} / \mathrm{h}\) ? At this speed, how long would it take to run \(1.00 \times\) \(10^{2}\) yards?

Short answer

Average Speed = \( \frac{100}{9.58} \: \mathrm{m/s} \) = 10.44 \( \mathrm{m/s} \)

Step-by-step solution

Convert Time to Average Speed in m/s

Given the world record for the hundred-meter dash is 9.58 seconds, to find the average speed, we can use the following formula: Average Speed = \( \frac{Distance}{Time} \) In this case, the distance is 100 meters, and the time is 9.58 seconds. So, the average speed will be: Average Speed = \( \frac{100 \: meters}{9.58 \: seconds} \)

Key concepts

Physics in Sports

Understanding the principles of physics is essential when analyzing sports performance, especially in events such as the hundred meter dash. This race is a great example of the concepts of displacement, velocity, and acceleration at play. In physics, speed is defined as the distance traveled per unit of time. It's an average measurement that doesn't take into account variations in speed over the distance covered.

In sprinting, athletes aim to maximize their velocity to achieve the shortest possible time over a set distance. Here, power, force, and energy conversion are important topics. Sprinters use their strength to generate force against the ground, propelling themselves forward. The principles of kinematics can be used to analyze their starting acceleration, maximum speed, and their deceleration as they cross the finish line.

Unit Conversion

To effectively communicate measurements in science, it's important to be comfortable with unit conversion, which allows us to express quantities in different units. For example, the world record in the hundred meter dash, expressed in seconds, may also be expressed in hours for different types of calculations. This can involve simple multiplication or division when converting within the metric system, like converting meters to kilometers, or more complex multiplication factors when switching between metric and imperial systems, such as meters to feet or miles.

To enhance understanding, it is valuable to practice unit conversion with measures commonly used in sports, such as converting a time given in seconds into minutes or hours, or distances from meters to yards. Mastering this skill makes comparisons and calculations more meaningful across various sports and everyday contexts.

Distance Time Relationship

The relationship between distance and time is fundamental to understanding motion in physics. This relationship is directly used to calculate speed. As we've seen in the step-by-step solution, average speed is simply the total distance divided by the total time taken to cover that distance. In the context of a hundred meter dash, it's clear that the faster a sprinter covers that distance, the shorter the time they take, resulting in a higher average speed.

The formula for average speed becomes a powerful tool in analyzing performance in sports. By knowing the distance and the average speed, one can calculate the time it takes for an athlete to complete a race, and vice versa. This relationship helps coaches and athletes in planning training regimes and predicting race outcomes.

Speed in Different Units

Speed can be expressed in multiple units, depending on the context and convention. For instance, in track events like the hundred meter dash, it is common to use meters per second (m/s). However, in different countries or sports, other units such as kilometers per hour (km/h) or miles per hour (mi/h) may be more convenient.

When you convert the average speed of a sprinter from one unit to another, you're often applying a conversion factor. For example, to convert m/s to km/h, you would multiply the original value by 3.6 (since there are 3600 seconds in an hour and 1000 meters in a kilometer). Conversely, to go from km/h to m/s, you divide by 3.6. Converting between metric and imperial units requires different factors, as the systems are not based on the same base units.