Question

Would a car traveling at a constant speed of \(65 \mathrm{~km} / \mathrm{h}\) violate a \(40 \mathrm{mi} / \mathrm{h}\) speed limit?

Short answer

The car's speed in miles per hour is \( 40.38 \ \mathrm{mi/h} \), which is greater than the speed limit of 40 mi/h. Therefore, the car would violate the 40 mi/h speed limit.

Step-by-step solution

Write down given values

We are given: - Car's speed: 65 km/h - Speed limit: 40 mi/h

Convert car's speed to miles per hour

To convert the car's speed from km/h to mi/h, we will use the conversion factor 1 km = 0.621371 mi. Car's speed in mi/h = \( 65 \ \mathrm{km/h} \times 0.621371 \ \dfrac{\mathrm{mi}}{\mathrm{km}} \)

Calculate car's speed in miles per hour

Multiply the car's speed in km/h by the conversion factor: Car's speed in mi/h = \( 65 \ \mathrm{km/h} \times 0.621371 \ \dfrac{\mathrm{mi}}{\mathrm{km}} = 40.38 \ \mathrm{mi/h} \)

Compare the car's speed to the speed limit

Now that we have the car's speed in mi/h, we can compare it to the speed limit (40 mi/h) to determine if it is exceeding the limit: 40.38 mi/h (Car's speed) > 40 mi/h (Speed limit)

Conclusion

Since the car's speed in miles per hour (40.38 mi/h) is greater than the given speed limit (40 mi/h), the car would indeed violate the 40 mi/h speed limit.

Key concepts

Understanding Speed Limits

Speed limits are essential for maintaining road safety. They are designed to prevent accidents and ensure smooth traffic flow. Essentially, a speed limit is the maximum legal speed at which you are allowed to travel on a particular road. Distances can vary based on road conditions and traffic regulations.

- Speed limits are often displayed in either miles per hour (mi/h) or kilometers per hour (km/h).
- Exceeding the speed limit can result in fines or other penalties.
- It's crucial to always be aware of the designated speed limit for the road you are traveling on.

In our exercise, understanding the speed limit allows us to determine if our car's speed of 65 km/h violates the 40 mi/h limit.

Converting Kilometers to Miles

Converting speed measurements between kilometers and miles is a common task, especially when traveling between countries that use different measurement systems. Here's how the conversion typically works:

- The standard conversion factor from kilometers to miles is 1 kilometer = 0.621371 miles.
- To convert, multiply the number of kilometers by this factor. For example, to convert 65 km/h to mi/h: \[65 imes 0.621371 = 40.38\] mi/h

This calculation shows the car's speed in miles per hour, allowing us to compare it with the speed limit (40 mi/h) directly. This way, you can determine if the car is speeding.

The Concept of Constant Speed

Constant speed refers to maintaining the same speed over a period of time. This means the car is not accelerating or decelerating.

- With constant speed, the distance traveled over each unit of time remains the same.
- For calculations, this simplifies problems because you don't have to account for changes in speed.

In our exercise, the car travels at a constant speed of 65 km/h. Using this information, we can easily convert to miles per hour and determine if it exceeds the 40 mi/h speed limit. Understanding constant speed makes it easier to analyze and predict the car's motion over time.