Question

Would an automobile moving at a constant speed of \(100 \mathrm{km} / \mathrm{h}\) violate a \(65-\mathrm{mph}\) speed limit?

Short answer

An automobile moving at a constant speed of 100 km/h is equivalent to approximately 62.14 mph. Since this speed is less than the 65-mph speed limit, the automobile would not be violating the speed limit.

Step-by-step solution

Convert km/h to mph

To convert the speed from km/h to mph, we can use the conversion factor: 1 km = 0.621371 miles. So, we need to multiply the given speed (100 km/h) by the conversion factor. \(100 \, \text{km/h} \times 0.621371 \, \frac{\text{miles}}{\text{km}}\)

Calculate the speed in mph

Now, let's do the multiplication: \(100 \times 0.621371 = 62.1371 \, \text{mph}\) So, the automobile's speed in mph is approximately 62.14 mph.

Compare the speed with the speed limit

To determine if the automobile is violating the 65-mph speed limit, we need to compare its speed (62.14 mph) with the speed limit (65 mph). Since the automobile's speed (approx. 62.14 mph) is less than the speed limit (65 mph), it is not violating the 65-mph speed limit. Therefore, an automobile moving at a constant speed of 100 km/h would not violate a 65-mph speed limit.

Key concepts

Kilometers to Miles Conversion

When dealing with distances, speeds, or other measurements, it's often necessary to convert between metric and imperial units—specifically, kilometers and miles. The basic conversion factor to remember is that 1 kilometer is equal to approximately 0.621371 miles. This is a crucial piece of information for converting speeds from kilometers per hour (km/h) to miles per hour (mph).

To perform a kilometers to miles conversion, multiply the number of kilometers by 0.621371. For example, if a vehicle is traveling at 100 km/h, its speed in miles per hour can be calculated by:

• Multiplying: \(100 imes 0.621371 = 62.1371 \text{ mph}\).

In general, having a firm grasp of this conversion factor simplifies many calculations in physics, especially when interpreting or comparing speeds.

Speed Limit Comparison

Understanding speed limits is crucial for safe and legal driving. In different parts of the world, speed limits may be posted in different units: kilometers per hour or miles per hour. Hence, converting the speed of a vehicle from one unit to another becomes essential when comparing against posted speed limits.

In our example, we need to determine whether a car moving at 100 kilometers per hour is exceeding a 65 miles per hour speed limit. By converting the car's speed, we find it moves at about 62.14 mph, which is lower than 65 mph. This means the vehicle is within the legal speed limit.

• Finding if speeds are below or above the limit can prevent tickets or potential accidents.
• Consistent conversions ensure accuracy in determining compliance with traffic laws.

Unit Conversion in Physics

In physics, converting units is a fundamental skill required to solve problems accurately. Whether in mechanics, electromagnetism, or thermodynamics, understanding how to interchange between units ensures seamless calculations. The method comprises understanding and applying the correct conversion factors.

Practically, unit conversion saves time and enhances precision in real-world applications like engineering, travel, and sports. For example, when dealing with speed or acceleration, converting between kilometers, miles, meters, and feet may be necessary to align with both SI and imperial systems.

In any unit conversion, remember to:

• Identify the necessary conversion factor (like kilometers to miles).
• Perform careful multiplication or division to achieve the desired unit.
• Double-check calculations to ensure reliability.

Mastering unit conversions not only clarifies problem-solving but also builds a strong foundation for advanced studies.