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

Young & Freedman Calc 15th Edition

Ch 02: Motion Along a Straight Line

Problem 26a

Chapter 2, Problem 26a

A cat walks in a straight line, which we shall call the $x$ -axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E $2.30$ ). Find the cat's velocity at $t equals 4.0$ s and at $t equals 7.0$ s.

Verified step by step guidance

Examine the first graph, which shows the velocity of the cat in meters per second (m/s) as a function of time in seconds (s). The velocity is represented by the red line.

To find the velocity at t = 4.0 s, locate 4.0 s on the horizontal time axis and move vertically to intersect the red line. Read the corresponding velocity value on the vertical axis.

Similarly, to find the velocity at t = 7.0 s, locate 7.0 s on the horizontal time axis and move vertically to intersect the red line. Read the corresponding velocity value on the vertical axis.

The second graph is not relevant to the problem as it is in different units (cm/s) and does not match the description of the problem. Focus on the first graph for the solution.

Ensure that the values read from the graph are interpreted correctly, considering the scale and units provided on the axes.

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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 an object's position with respect to time. It has both magnitude and direction, indicating how fast an object is moving and in which direction. In this context, the cat's velocity is measured in centimeters per second (cm/s) along the x-axis.

Velocity-Time Graph

A velocity-time graph visually represents an object's velocity as a function of time. The slope of the graph indicates acceleration, while the area under the curve represents displacement. In the provided graph, the linear decrease in velocity suggests that the cat is decelerating until it reaches a negative velocity, indicating a change in direction.

Linear Motion

Linear motion refers to the movement of an object along a straight path. In this scenario, the cat's motion is described as linear along the x-axis, with its velocity changing uniformly over time. Understanding linear motion is essential for analyzing the cat's velocity at specific time intervals, such as at 4.0 seconds and 7.0 seconds.

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Related Practice

Textbook Question

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of $20$ m/s ( $45$ mi/h) when it reaches the end of the $120$ -m-long ramp. How much time does it take the car to travel the length of the ramp?

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Textbook Question

A cat walks in a straight line, which we shall call the $x$ -axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E $2.30$ ). What distance does the cat move during the first $4.5$ s? From $t equals 0$ to $t equals 7.5$ s?

A cat walks in a straight line, which we shall call the $x$ -axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E $2.30$ ). What is the cat's acceleration at $t equals 3.0$ s? At $t equals 6.0$ s? At $t equals 7.0$ s?

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Textbook Question

A cat walks in a straight line, which we shall call the $x$ -axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E $2.30$ ). Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.

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Textbook Question

The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than $250$ m/s². If you are in an automobile accident with an initial speed of $105$ km/h ( $65$ mi/h) and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

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