Converting Speed from Kilometers per Hour to Meters per Second: A Comprehensive Guide

Understanding how to convert speed from kilometers per hour (km/hr) to meters per second (m/s) is crucial in various fields such as transportation, physics, and engineering. In this article, we will explore a detailed method to calculate the speed of a school bus using the distance and time given. Let's dive into the step-by-step process.

Understanding the Problem

We are given:

Distance covered by the school bus: 16 kilometers (km) Time taken to cover the distance: 40 minutes

The goal is to find the speed of the school bus in both m/s and km/hr.

Step-by-Step Solution

Converting Time to Hours

The first step is to convert the time from minutes to hours since the speed formula uses hours as the unit of time.

Given time 40 minutes

Time in hours (40 / 60 2 / 3) hours (approximately 0.667 hours)

Calculating Speed in Kilometers per Hour (km/hr)

The formula for speed in km/hr is:

(Speed (km/hr) frac{Distance (km)}{Time (hours)})

Substituting the given values:

(Speed (km/hr) frac{16 km}{2 / 3 hr} 16 times frac{3}{2} 24 km/hr)

Converting Distance to Meters

To calculate speed in m/s, we need to convert the distance from kilometers to meters.

Distance in meters 16 km times 1000 16000 meters

Converting Time to Seconds

Next, we convert the time from hours to seconds.

Time in seconds 40 minutes times 60 2400 seconds

Calculating Speed in Meters per Second (m/s)

The formula for speed in m/s is:

(Speed (m/s) frac{Distance (m)}{Time (seconds)})

Substituting the converted values:

(Speed (m/s) frac{16000 m}{2400 s} frac{16000}{2400} approx 6.67 m/s)

Summary of the Results

The speed of the school bus can be expressed in two units:

Speed in km/hr: 24 km/hr Speed in m/s: 6.67 m/s

Additional Explanations and Conversion Methods

Similar Problems

To further solidify our understanding, let's look at a few more conversion problems:

Time 45 minutes frac{45}{60} frac{3}{4} hour Distance 27 km

Speed in km/hr:

(Speed frac{27 km}{frac{3}{4} hour} 27 times frac{4}{3} 36 km/hr)

Speed in m/s:

(Speed frac{27 times 1000}{3600} 7.5 m/s)

Another example with speed given in km/hr and converted to m/s:

Speed 36 km/hr frac{36 times 1000}{3600} 10 m/s

Alternative Conversion Method

Another way to approach the problem is:

Time 40 minutes frac{40}{60} frac{2}{3} hour

Distance 16 km

Speed in km/hr:

(Speed frac{16}{frac{2}{3}} 24 km/hr)

Speed in m/s:

(Speed frac{16000}{2400} approx 6.67 m/s)

Conclusion

By following the methods outlined in this guide, you can easily convert speed from km/hr to m/s, and vice versa. Whether you're dealing with school buses, cars, or any other vehicle, understanding this conversion is essential for accurate calculations and problem-solving.

For more related resources and examples, you can explore additional materials on topics like velocity, distance, and time in physics and engineering.