Calculating Distance Traveled by a Bus: A Comprehensive Guide

In this article, we will delve into the process of calculating the distance that a bus would travel using basic mathematical methods. This concept is fundamental for understanding various real-world applications, such as travel planning, transportation engineering, and basic physics problems.

Understanding the Problem

Let's consider the initial problem: A private bus travels 25 kilometers per hour (km/h). If the bus is in motion for 4.5 hours, what distance would it cover?

The formula for distance is given by:

Distance Speed × Time

To solve the problem, we will follow the conventional method, which involves multiplication of the speed (25 km/h) by the time (4.5 hours).

Step-by-Step Solution:

1. **Speed** 25 km/h

2. **Time** 4.5 h

Distance traveled 25 km/h × 4.5 h 112.5 km

Dimensional Analysis and Unit Cancellation

Another way to approach such problems is through dimensional analysis, also known as unit cancellation or unit factor. This method helps in ensuring that the units are consistent and makes it easier to solve complex problems.

Method 1:

We can express the time in hours and the speed in kilometers per hour and then multiply:

4.5 h × 25 km/1 h 112.5 km

This shows that the hours unit cancels out, leaving the distance in kilometers.

Method 2:

Using a formula that you would have memorized:

Distance Speed × Time 25 km/h × 4.5 h 112.5 km

Tying in Real-World Contexts

While the problem seems straightforward, it’s important to note that speed is always relative and makes use of a datum reference point. Speed can be significantly affected by factors such as the rotation of the Earth (up to 1,500 km/h), the orbital velocity of the Earth (around 29.78 km/s), and the speed of the sun through interstellar medium (ISM) and around the galaxy. However, for the sake of this calculation, we assume that these factors have a negligible effect on the results.

Let's explore a few related problems to solidify our understanding:

Example 1:

If a bus travels at a speed of 20 meters per second (m/s), how far would it travel in 4.5 hours?

Steps:

Convert the speed from m/s to km/h:20 m/s × 3600 s/h 72000 m/h 72 km/hMultiply the speed by the time:72 km/h × 4.5 h 288 km

Example 2:

If a bus travels at 20 meters per second, how far does it travel in 4 hours?

Steps:

Convert the speed from m/s to km/h:20 m/s 72 km/hMultiply the speed by the time:72 km/h × 4 h 288 km

Example 3:

If a bus moves at a speed of 20 m/s:

1 second 20 meters4 hours 4 × 3600 seconds 14400 secondsDetermine the distance in meters:20 m/s × 14400 s 288000 mConvert the distance to kilometers:288000 m ÷ 1000 288 km

Conclusion

Understanding how to calculate distance traveled is a crucial skill for basic physics and mathematics. By following the steps of dimensional analysis and using the distance formula, we can solve a wide range of similar problems. It's important to remember that speed and distance calculations, while being foundational, can be significantly influenced by real-world factors such as the Earth's rotation and orbital velocity.

By mastering these techniques, you can approach more complex problems with confidence.