Problem 5 - An Introduction to Physical Science

Question

A group of college students eager to get to Florida on a spring break drove the 750 -mi trip with only minimum stops. They computed their average speed for the trip to be \(55.0 \mathrm{mi} / \mathrm{h}\). How many hours did the trip take?

Step-by-Step Solution

Answer

The trip took approximately 13.64 hours.

Step 1: Understand the Problem

We need to find out how many hours it took for a trip of 750 miles at an average speed of 55 miles per hour.

Step 2: Recall the Formula for Time

The formula to find time when distance and speed are known is \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).

Step 3: Plug Values into the Formula

Substitute the given values into the formula: \( \text{Time} = \frac{750}{55} \).

Step 4: Calculate the Time

Divide 750 by 55 to get the time: \( \frac{750}{55} \approx 13.64 \) hours.

Step 5: Interpret the Result

The calculation means the trip took approximately 13.64 hours to complete.

Key Concepts

Average Speed

Average speed is a fundamental concept when talking about motion and travel. It explains how quickly something is moving on average over its journey. In the context of a road trip, like the one the college students took, average speed is calculated by dividing the total distance traveled by the total time taken. This is crucial because it offers a straightforward way of understanding movement over long distances.

Here's how to make sense of average speed:

• Average speed considers the entire journey, not just parts of it.
• It's a scalar quantity, meaning it has magnitude but no direction.
• Even if your speed varies over time, the average speed smooths out these variations.

For example, the students drove 750 miles at an average speed of 55 miles per hour. This average accounts for any speed changes, stops, or slow downs, providing a simple view of the entire trip."

Distance-Rate-Time Relationship

This relationship is the backbone of calculating travel scenarios like the students' spring break trip. It interconnects three key variables: distance, rate (or speed), and time. They are connected through the formula: \[\text{Time} = \frac{\text{Distance}}{\text{Speed}} \]Understanding how to manipulate this formula is essential in physics and real-life problem solving.

Here’s what to remember:

• If you know any two of the variables, you can find the third.
• The formula can be rearranged to find distance or speed.
• It assumes steady speed over the travel time, making it easy for average calculations.

Consider the simple approach to find how long the 750-mile journey at 55 miles per hour took. By plugging these into the formula, you find that the time taken is approximately 13.64 hours. This demonstrates the utility of the distance-rate-time relationship in real-world situations."

Unit Conversion

Unit conversion is important because it ensures all pieces of data fit together properly in calculations. When discussing speed and distance, units like miles and hours are commonly used, but converting units can sometimes be necessary.

Here’s why unit conversion is useful:

• Ensures consistency across measurements.
• Helps in converting units to match what’s asked for in a problem.
• Makes data compatible for comparison and further calculations.

Although the exercise here didn't require conversions between miles and kilometers or hours and minutes explicitly, understanding conversions can be handy. It allows one to interpret distances or times in different units or even convert speeds such as from miles per hour to kilometers per hour if needed."