Understanding Speed and Distance: Calculating Feet Travelled

When it comes to understanding the movement of a bicycle at a specific speed, one common question that may arise is: 'How far will a bicycle traveling at 13 miles per hour go in 47 seconds?' This article will delve into the methods and formulas used to calculate such distances, providing a comprehensive guide for readers to understand these calculations more effectively.

Converting Units and Calculation Steps

To find out how far a bicycle traveling at 13 miles per hour (mph) goes in 47 seconds, the following steps are essential:

1. Converting Miles per Hour to Feet per Second (fps)

First, we need to convert miles per hour into feet per second. There are 5280 feet in a mile and 3600 seconds in an hour. The conversion can be done using the formula:

feet per second miles per hour x ( frac{5280 text{ feet}}{1 text{ mile}} times frac{1 text{ hour}}{3600 text{ seconds}} )

For a bicycle traveling at 13 mph, the calculation is as follows:

feet per second 13 x ( frac{5280}{3600} ) ( approx 19.07 text{ fps} )

2. Calculating the Distance Traveled in 47 Seconds

Using the formula for calculating distance, which is:

distance speed x time

We can now calculate the distance covered by the bicycle in 47 seconds:

distance 19.07 text{ fps} x 47 text{ seconds} ( approx 895.29 text{ feet} )

This means a bicycle traveling at 13 mph will cover approximately 895.29 feet in 47 seconds.

Additional Examples and Calculations

Let's consider another example to further illustrate these calculations. If a bicycle is traveling at 12 miles per hour (mph), how many feet will it cover in 45 seconds? Here’s a step-by-step breakdown:

1. Converting 12 mph to Feet per Second (fps)

There are 5280 feet in a mile and 3600 seconds in an hour. So:

12 miles/hr 12 miles/3600 sec 12/3600 miles/second 1/300 miles/second 5280/300 feet/sec 88/5 feet/sec

Then, to find the distance covered in 45 seconds:

distance 88/5 ft/sec x 45 sec 792 feet

Therefore, a bicycle traveling at 12 mph will cover approximately 792 feet in 45 seconds.

Further Thoughts and Tips

Calculating the speed of a bicycle in feet per second can be useful in various scenarios. Whether it's for homework, recreational purposes, or professional applications, understanding these calculations can save time and reduce uncertainty.

Perhaps you might encounter a question like: '12 cdot frac{22}{15} cdot 45'. If this is a homework problem, ensure you show your work and explain the calculations in detail as the middle fraction is likely a key part of the solution.

Remember that there are 5280 feet in a mile. So, to convert 12 miles to feet per hour, first, calculate the feet in 12 miles:

12 miles/hr 12 x 5280 feet/hr 63360 feet/hr - Then, convert this to feet per second:

63360/3600 17.6 feet/sec

To find the distance in 45 seconds, simply multiply 17.6 by 45:

17.6 x 45 792 feet

This confirms the earlier calculation and demonstrates the consistency of using these conversion methods.

Conclusion

Understanding and mastering the conversion of speed from miles per hour to feet per second can greatly enhance your problem-solving skills when dealing with distances covered by bicycles or any other moving objects. By following the steps outlined in this article, you can perform these conversions with ease, ensuring accuracy and reliability in your calculations.

Frequently Asked Questions

Q: How many feet will a bicycle traveling at 12 mph cover in 45 seconds?

A: A bicycle traveling at 12 mph will cover approximately 792 feet in 45 seconds.

Q: What is the formula to convert miles per hour to feet per second?

A: The formula is: feet per second miles per hour x ( frac{5280 text{ feet}}{1 text{ mile}} times frac{1 text{ hour}}{3600 text{ seconds}} )

Q: How do you calculate the distance traveled in a given time?

A: The formula for distance is: distance speed x time.