Starting from the front door of a ranch house, you walk m due east to a windmill, turn around, and then slowly walk m west to a bench, where you sit and watch the sunrise. It takes you s to walk from the house to the windmill and then 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 Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 2, Problem 3
You normally drive on the freeway between San Diego and Los Angeles at an average speed of km/h ( mi/h), and the trip takes h and min. On a Friday afternoon, however, heavy traffic slows you down and you drive the same distance at an average speed of only km/h ( mi/h). How much longer does the trip take?
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First, convert the time of the normal trip from hours and minutes to hours. The trip takes 1 hour and 50 minutes, which is equivalent to 1 + 50/60 hours.
Calculate the distance of the trip using the formula for distance: \( \text{Distance} = \text{Speed} \times \text{Time} \). Use the normal speed of 105 km/h and the converted time from step 1.
Now, calculate the time taken for the trip on Friday afternoon using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \). Use the distance calculated in step 2 and the reduced speed of 70 km/h.
Convert the time taken on Friday afternoon from hours to hours and minutes for easier comparison with the normal trip time.
Finally, find the difference in time between the normal trip and the Friday afternoon trip by subtracting the normal trip time from the Friday afternoon trip time. This will give you how much longer the trip takes.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Average Speed
Average speed is defined as the total distance traveled divided by the total time taken to travel that distance. It is a scalar quantity and is typically expressed in units such as kilometers per hour (km/h) or miles per hour (mi/h). Understanding average speed is crucial for calculating travel time over a given distance.
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Distance-Time Relationship
The distance-time relationship is a fundamental concept in kinematics, which states that distance equals speed multiplied by time (d = vt). This relationship allows us to calculate one of these variables if the other two are known, making it essential for solving problems involving travel time and speed.
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Unit Conversion
Unit conversion involves changing a measurement from one unit to another, such as converting time from hours and minutes to just hours. This is important for ensuring consistency in calculations, especially when dealing with different units of speed and time, as seen in this problem where time is given in hours and minutes.
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Related Practice
Textbook Question
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Textbook Question
A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by , where m/s2 and m/s3. Calculate the instantaneous velocity of the car at , s, and s.
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Textbook Question
In an experiment, a shearwater (a seabird) was taken from its nest, flown km away, and released. The bird found its way back to its nest days after release. If we place the origin at the nest and extend the –axis to the release point, what was the bird's average velocity in m/s for the return flight?
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Textbook Question
A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by , where m/s2 and m/s3. Calculate the average velocity of the car for the time interval to s.
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