Problem 60 - Chemistry: An Atoms-Focused Approach

Question

In 1973 a horse named Secretariat ran the fastest Kentucky Derby in history, taking 1 minute and 59.4 seconds to run 1.25 miles. What was Secretariat's average speed in (a) miles per hour and (b) meters per second?

Step-by-Step Solution

Answer

Answer: (a) Secretariat's average speed in miles per hour is 37.54 mph. (b) Secretariat's average speed in meters per second is 16.77 m/s.

Step 1: Convert the given time into a single unit (either minutes or seconds)

Convert the given time into seconds: 1 minute = 60 seconds. So, the total time taken is 1 * 60 + 59.4 = 119.4 seconds.

Step 2: Find the average speed in miles per hour

Using the formula average speed = total distance / total time, we have average speed = 1.25 miles / (119.4 seconds). Since we need the average speed in miles per hour, we will convert the time from seconds to hours: 119.4 seconds = 119.4/3600 hours. So, the average speed = 1.25 miles / (119.4/3600 hours) = 1.25 * (3600/119.4) mph ≈ 37.54 mph.

Step 3: Convert miles per hour to meters per second

We know that 1 mile ≈ 1609.34 meters and 1 hour = 3600 seconds. Therefore, to convert the speed from miles per hour to meters per second, we can use the conversion factor: (1 mile / hour) * (1609.34 meters / 1 mile) * (1 hour / 3600 seconds) = (1609.34 meters / 3600 seconds) = 0.44704 m/s. Now, multiply this conversion factor by the average speed in miles per hour to get the average speed in meters per second: 37.54 mph * 0.44704 (m/s / mph) ≈ 16.77 m/s.

Step 4: Write down the final answer

(a) Secretariat's average speed in miles per hour is 37.54 mph. (b) Secretariat's average speed in meters per second is 16.77 m/s.

Key Concepts

Understanding Unit Conversion

When solving problems related to average speed, understanding unit conversion is vital. Unit conversion is the process of converting one unit of measurement to another. For example, if you're given time in minutes, but you need the speed in miles per hour, you'll need to change the time unit to hours.

Here are some basic conversions you should know:

• 1 minute is equal to 60 seconds.
• 1 hour is equal to 3600 seconds.
• 1 mile is approximately 1609.34 meters.

Using these conversions, you can easily move between time and distance units needed to calculate speed, ensuring accuracy in your calculations. This is especially useful when comparing different speeds in various units!

What is Miles per Hour?

Miles per hour (mph) is a unit of speed commonly used in the United States. It measures how many miles an object can travel in one hour.

To find speed in miles per hour, use the formula:
\[ \text{Speed (mph)} = \frac{\text{Total Distance (miles)}}{\text{Total Time (hours)}} \]

In the problem we’re discussing, Secretariat’s run was originally measured in seconds, so we converted those seconds into hours to calculate miles per hour. It’s important to remember that whenever you're given distances in miles and time in seconds, you must know how to convert seconds into hours to use the formula properly. This kind of unit conversion is essential in everyday life, even beyond horse racing!

What Does Meters per Second Mean?

Meters per second (m/s) is the speed unit used in the metric system, favored in scientific contexts worldwide. It indicates how many meters an object travels in one second.

To convert miles per hour to meters per second, first convert miles to meters and hours to seconds using these factors:

• 1 mile = 1609.34 meters
• 1 hour = 3600 seconds

Then use the formula:
\[ \text{Speed (m/s)} = \text{Speed (mph)} \times 0.44704 \]

This conversion applies whether calculating the speed of a horse or a car, offering a familiar format for those using the metric system. Understanding how to switch between these units is key for effective communication across different fields and regions.

Horse Racing and Speed

Horse racing is a sport where speed and time are crucial for determining success. Understanding how to calculate and compare speeds in different units becomes important in a sport where records are often set with precise timings.

For example, Secretariat’s record-breaking performance in the Kentucky Derby is often compared using mph and m/s to accommodate both American and international audiences.

Knowing how to switch between these units can also provide you with greater insights when analyzing historical races, comparing speeds, and appreciating the achievements of remarkable horses like Secretariat. Additionally, being able to calculate average speed helps enthusiasts and professionals alike to predict outcomes and improve training techniques.