Starting from the front door of a ranch house, you walk 60.060.0 m due east to a windmill, turn around, and then slowly walk 40.040.0 m west to a bench, where you sit and watch the sunrise. It takes you 28.028.0 s to walk from the house to the windmill and then 36.036.0 s to walk from the windmill to the bench. For the entire trip from the front door to the bench, what are your (a) average velocity? (b) average speed?

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problem 5

Chapter 2, Problem 5

Starting from the front door of a ranch house, you walk $60.0$ m due east to a windmill, turn around, and then slowly walk $40.0$ m west to a bench, where you sit and watch the sunrise. It takes you $28.0$ s to walk from the house to the windmill and then $36.0$ s to walk from the windmill to the bench. For the entire trip from the front door to the bench, what are your (a) average velocity? (b) average speed?

Verified step by step guidance

Step 1: Understand the problem and identify the key quantities. The total displacement is the straight-line distance from the starting point (front door) to the final position (bench). Since you walk 60.0 m east and then 40.0 m west, the net displacement is calculated as: $ \text{Displacement} = 60.0 \ \text{m} - 40.0 \ \text{m} $.

Step 2: Calculate the total distance traveled. The total distance is the sum of the distances walked in both directions: $ \text{Total Distance} = 60.0 \ \text{m} + 40.0 \ \text{m} $.

Step 3: Determine the total time taken for the trip. Add the time taken to walk from the house to the windmill and the time taken to walk from the windmill to the bench: $ \text{Total Time} = 28.0 \ \text{s} + 36.0 \ \text{s} $.

Step 4: Calculate the average velocity. Average velocity is defined as the total displacement divided by the total time: $ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}} $. Use the displacement from Step 1 and the total time from Step 3.

Step 5: Calculate the average speed. Average speed is defined as the total distance traveled divided by the total time: $ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $. Use the total distance from Step 2 and the total time from Step 3.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. Displacement is a vector quantity that considers the shortest straight-line distance from the initial to the final position, along with its direction. In this scenario, the average velocity will be calculated by determining the net change in position from the starting point to the bench and dividing it by the total time taken for the entire journey.

Average Speed

Average speed is a scalar quantity that measures the total distance traveled divided by the total time taken, regardless of direction. It provides an overall measure of how fast an object is moving during a trip. In this case, to find the average speed, one must sum the distances walked to the windmill and the bench, and then divide that sum by the total time spent walking.

Displacement vs. Distance

Displacement and distance are two important concepts in physics that describe motion. Distance is the total path length traveled, while displacement is the straight-line distance from the starting point to the endpoint, including direction. Understanding the difference between these two concepts is crucial for accurately calculating average velocity and average speed in the given problem.

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Displacement vs. Distance

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