Calculating the Speed of a Car in km/h and m/s

Speed is a fundamental concept in physics and everyday life, often measured and expressed in different units such as kilometers per hour (km/h) and meters per second (m/s). In this article, we will explore how to calculate the speed of a car that travels a certain distance in a given time, providing detailed steps and conversions. This will help you understand the conversion between these units and the underlying physics concepts.

Problem Setup: A Car Travels 15 km in 20 Minutes

Imagine a car that covers a distance of 15 kilometers in 20 minutes. In physics, this problem can be simplified by breaking it down into smaller, manageable steps. We'll follow these steps to find the speed in both km/h and m/s.

Step 1: Convert Time to Hours for km/h Calculation

To calculate the speed in kilometers per hour (km/h), we first need to express the time in hours. We know that 20 minutes is a fraction of an hour, specifically 20/60, which simplifies to 1/3 of an hour.

Mathematical Steps:

Time in hours: 20/60 1/3 ≈ 0.333 hours

Step 2: Calculate Speed in km/h

The formula for calculating speed in km/h is straightforward: Speed Distance / Time. In this case, the distance is 15 kilometers and the time is 1/3 hours.

Calculation: [ text{Speed}_{text{km/h}} frac{15 text{ km}}{frac{1}{3} text{ h}} 15 times 3 45 text{ km/h} ]

Step 3: Convert Distance and Time to m and s for m/s Calculation

For calculating speed in meters per second (m/s), we need to convert the distance from kilometers to meters and the time from minutes to seconds. We know that 1 kilometer is equal to 1000 meters and 1 minute is equal to 60 seconds.

Mathematical Steps:

Convert distance from kilometers to meters: 15 km 15 × 1000 m 15000 m

Convert time from minutes to seconds: 20 minutes 20 × 60 seconds 1200 seconds

Step 4: Calculate Speed in m/s

Using the formula for calculating speed in m/s (Speed Distance / Time), we now have the distance in meters and time in seconds. Plugging these values into the formula, we get:

Calculation: [ text{Speed}_{text{m/s}} frac{15000 text{ m}}{1200 text{ s}} frac{15000}{1200} frac{15000 div 600}{1200 div 600} frac{25}{2} 12.5 text{ m/s} ]

Final Speeds

The speed of the car can be expressed in both units:

45 km/h 12.5 m/s

Conclusion

In summary, we have calculated the speed of a car that travels 15 kilometers in 20 minutes and converted the result to both kilometers per hour (km/h) and meters per second (m/s). By following these steps, you can easily calculate speed in different units and understand the underlying principles of speed calculations in physics.

Quick Reference

For future reference, the conversions used in this problem are:

1 km 1000 meters (m) 1 hour 60 minutes (min) 3600 seconds (s) Speed in km/h (frac{text{Distance in km}}{text{Time in hours}}) Speed in m/s (frac{text{Distance in meters}}{text{Time in seconds}})

Additional Tips

When dealing with speed problems, always ensure that your units are consistent. Use unit cancellation and conversion factors to make the calculations easier and more accurate. This method is particularly useful when you're unsure about the problem.

Remember, understanding the underlying concepts and practicing similar problems will help you master the art of speed calculations in various units.