Calculating Distance Traveled by a Car at 90 km/h in 10 Minutes

Understanding the distance traveled by a car at a specific speed over a given time is a fundamental skill in physics and everyday problem-solving. This article will walk you through the process of calculating how far a car travels in 10 minutes when it's traveling at a steady speed of 90 km/h. We'll explore various methods to ensure a comprehensive understanding of the concept.

Introduction to Units and Conversions

Let's begin with a brief introduction to units and conversions. When working with speeds and distances, it's essential to understand the relationship between kilometers per hour (km/h) and meters per second (m/s), as well as the relationship between minutes and seconds.

Converting Speed from km/h to m/s

The speed of the car is given in kilometers per hour, but to perform the calculation, we need to convert this into meters per second. The conversion factor is based on the fact that 1 kilometer is equal to 1000 meters, and 1 hour is equal to 3600 seconds. Therefore:

120 km/h 120 * 1000 m / 3600 s 33.33 m/s

Converting Time from Minutes to Seconds

Next, we need to convert the time from minutes to seconds. Since 1 minute is equal to 60 seconds:

10 minutes 10 * 60 s 600 s

Calculating Distance Using the Formula

With the speed in meters per second and the time in seconds, we can now use the formula for distance:

Distance Speed × Time

Substituting the values:

Distance 33.33 m/s × 600 s 20000 meters

Therefore, the car covers 20000 meters, or 20 kilometers, in 10 minutes.

Alternative Methods for Calculation

Another approach to solving this problem is to convert the speed into kilometers per minute and then multiply by the time in minutes. This method simplifies the calculation:

Conversion to Kilometers per Minute

Since there are 60 minutes in an hour:

10 minutes 1/6 hours

Now, using the formula:

Distance Speed × Time

Distance 90 km/h × 1/6 hours 15 km

Thus, the car travels 15 kilometers in 10 minutes.

Simpler Method Using Ratios

A simpler method involves recognizing that 10 minutes is 1/6 of an hour. Therefore, the distance traveled is:

Distance 90 km/h × 1/6 15 km

Additionally, since 10 minutes is 1/4 of 60 minutes, we can use a ratio to find the distance:

90 × 1/4 22.5 km

However, this is an overestimate, as the actual time is 10 minutes, not a full quarter of an hour.

Mastering Unit Conversion Techniques

To solve similar problems effortlessly, mastering unit cancellation and dimensional analysis is crucial. This technique allows you to convert units systematically and correctly. For example:

15 min * (1 h / 60 min) * (90 km / 1 h) 22.5 km

Using this method, you can easily and accurately convert between different units of measurement.

Remember, the key to mastering any problem-solving skill is practice. By understanding and applying these techniques, you'll be better equipped to tackle a variety of problems with confidence.

Conclusion

Understanding how to calculate the distance traveled by a car at a specific speed over a given time is essential for various applications, from everyday problem-solving to more advanced physics calculations. By mastering the conversion techniques and using the right formula, you can find the distance traveled in any given scenario.