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Ch 02: Motion Along a Straight Line
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 2, Problem 10a

A physics professor leaves her house and walks along the sidewalk toward campus. After 55 min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.102.10. At which of the labeled points is her velocity zero?
Position-time graph showing a curve with labeled points I to V; velocity is zero at point IV.

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1
To determine where the velocity is zero, we need to identify where the slope of the distance-time graph is zero. This occurs at points where the graph has a horizontal tangent.
Examine the graph and look for points where the curve is flat, indicating no change in distance over time.
Point 'b' on the graph is a peak, where the slope changes from positive to negative, indicating a momentary stop in movement. This is a point where the velocity is zero.
Point 'e' is another location where the graph levels off, indicating the professor has returned home and stopped moving, resulting in zero velocity.
Thus, the velocity is zero at points 'b' and 'e' on the graph.

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Key Concepts

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

Velocity

Velocity is a vector quantity that refers to the rate at which an object changes its position. It is defined as the derivative of position with respect to time. In a position-time graph, the velocity is represented by the slope of the graph. A zero velocity indicates that the object is momentarily at rest, which corresponds to a horizontal tangent line on the graph.
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Position-Time Graph

A position-time graph displays how an object's position changes over time. The x-axis typically represents time, while the y-axis represents position. The slope of the graph at any point gives the object's velocity at that time. A flat, horizontal section of the graph indicates that the object is not changing its position, meaning its velocity is zero.
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Slope of a Graph

The slope of a graph at a particular point is a measure of how steep the line is at that point. In the context of a position-time graph, the slope represents the object's velocity. A positive slope indicates motion in the positive direction, a negative slope indicates motion in the opposite direction, and a zero slope indicates no motion, meaning the velocity is zero.
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Related Practice
Textbook Question

A physics professor leaves her house and walks along the sidewalk toward campus. After 55 min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.102.10. At which of the labeled points is her velocity constant and positive?

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Textbook Question

A physics professor leaves her house and walks along the sidewalk toward campus. After 55 min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.102.10. At which of the labeled points is her velocity constant and negative?

3
views
Textbook Question

A physics professor leaves her house and walks along the sidewalk toward campus. After 55 min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.102.10. At which of the labeled points is her velocity decreasing in magnitude?

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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 x(t)=bt2ct3x(t)=bt^2-ct^3, where b=2.40b = 2.40 m/s2 and c=0.120c = 0.120 m/s3. Calculate the instantaneous velocity of the car at t=0t = 0, t=5.0t = 5.0 s, and t=10.0t = 10.0 s.

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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 x(t)=bt2ct3x(t)=bt^2-ct^3, where b=2.40b = 2.40 m/s2 and c=0.120c = 0.120 m/s3. Calculate the average velocity of the car for the time interval t=0t = 0 to t=10.0t = 10.0 s.

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Textbook Question

A ball moves in a straight line (the xx-axis). The graph in Fig. E2.92.9 shows this ball's velocity as a function of time. What are the ball's average speed and average velocity during the first 3.03.0 s?

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