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Ch 02: Motion Along a Straight Line
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 2, Problem 10c

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?
Position-time graph showing a curve with labeled points I to V; velocity is zero at point IV.

Verified step by step guidance
1
To determine where the velocity is constant and negative, we need to analyze the slope of the distance-time graph. A constant velocity corresponds to a straight line segment on the graph.
A negative velocity indicates that the slope of the line is negative, meaning the line is sloping downwards as time progresses.
Examine the graph and identify the segments where the line is straight and sloping downwards. This will indicate a constant negative velocity.
From the graph, observe the segment between points 'c' and 'b'. This segment is a straight line with a negative slope, indicating a constant negative velocity.
Therefore, the velocity is constant and negative between points 'c' and 'b'.

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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 describes the rate of change of position with respect to time, including both speed and direction. In the context of the graph, velocity is represented by the slope of the line. A constant negative velocity indicates a straight line with a downward slope, showing movement in the opposite direction.
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Position-Time Graph

A position-time graph displays an object's position relative to time, allowing analysis of motion characteristics such as velocity and acceleration. The slope of the graph at any point indicates the object's velocity. A negative slope signifies movement back toward the starting point, while a constant slope indicates uniform motion.
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Slope of a Line

The slope of a line on a graph represents the rate of change between the variables on the axes. In a position-time graph, the slope corresponds to velocity. A negative slope indicates a decrease in position over time, meaning the object is moving back toward its starting point. A constant slope implies uniform velocity.
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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 zero?

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views
Textbook Question

A turtle crawls along a straight line, which we will call the xx-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t)=50.0x(t) = 50.0 cm + (2.002.00 cm/s)tt − (0.06250.0625 cm/s2)t2t^2. At what time tt is the velocity of the turtle zero?

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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 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 turtle crawls along a straight line, which we will call the xx-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t)=50.0x(t) = 50.0 cm + (2.002.00 cm/s)tt − (0.06250.0625 cm/s2)t2t^2. Find the turtle's initial velocity, initial position, and initial acceleration.

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