Understanding the Speed Comparison Between Two Cars Based on Their Wheel Revolution Rates

This article explores how to calculate the speed of two cars based on the diameter of their wheels and their respective revolution rates. By applying mathematical principles and formulas, we can determine the relative speed of each car and the ratio between them.

Introduction to Wheel Revolution Rates

Two cars are in motion, each with different-sized wheels and distinct revolution rates. Let's delve into the details of these cars and how their wheel characteristics influence their speed.

Car1: 20-inch Diameter Wheels

The first car has wheels with a diameter of 20 inches. The circumference of each wheel (C) can be calculated using the formula C πd, where d is the diameter.

C πd 20π 62.83 inches per revolution (in/rev)

If this car's wheels make 24 revolutions per minute, the distance traveled per minute can be calculated as follows:

C 62.83 in/rev × 24 rev/min 1507.9 in/min

Car2: 30-inch Diameter Wheels

The second car has wheels with a diameter of 30 inches. Similarly, the circumference of these wheels is calculated as:

C πd 30π 94.25 inches per revolution (in/rev)

With a revolution rate of 18 revolutions per minute, the distance traveled per minute is:

C 94.25 in/rev × 18 rev/min 1696.5 in/min

Calculating the Speed Ratios

To find the ratio of the speed of the second car to that of the first, we compare their speed values:

Speed of Car2 / Speed of Car1 1696.5 in/min / 1507.9 in/min 1.125

This value can also be expressed as a ratio:

1 and 1/8 or 9/8

Further Analysis of Speed Ratios

Using the revolutions per minute rates directly, we can calculate the speed ratio as follows:

Ratio of Speed (18 rev/min × 30 in/rev) / (20 in/rev × 24 rev/min) 1.125 : 1

Converting to Kilometers Per Hour (kph)

To convert the speed from inches per minute to kilometers per hour, we use the conversion factor: 1 inch per minute ≈ 2.286 × 10-5 kilometers per hour.

The speed of Car1 in kph:

20π in/min × 24 rev/min × 2.286 × 10-5 kph/in/min 2.3 kph

The speed of Car2 in kph:

30π in/min × 18 rev/min × 2.286 × 10-5 kph/in/min 2.585 kph

Conclusion

By understanding the relationship between wheel diameter and revolutions per minute, and how they affect the speed of a car, we can accurately determine the relative speeds of two cars. This analysis is crucial for various applications, including vehicle engineering, race strategies, and even basic educational purposes.

Key Takeaways:

The circumference of a wheel is πd. The speed of a car can be calculated by multiplying the circumference by the revolution rate. The ratio of speeds can be determined by comparing their calculated distances.

Understanding these principles can help in making informed decisions about vehicle performance and efficiency.