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Ch 02: Kinematics in One Dimension
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 02: Kinematics in One DimensionProblem 4c
Chapter 2, Problem 4c

FIGURE EX2.4 is the position-versus-time graph of a bicycle. What is the bicycle's velocity at t = 30s?

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Step 1: Understand the concept of velocity. Velocity is the rate of change of position with respect to time. For a position-versus-time graph, the velocity at a specific time is determined by finding the slope of the tangent line to the graph at that time.
Step 2: Locate the point on the graph corresponding to t = 30s. Identify the position of the bicycle at this time by reading the graph carefully.
Step 3: Draw a tangent line to the curve at t = 30s. The tangent line represents the instantaneous rate of change of position at that specific time.
Step 4: Calculate the slope of the tangent line. The slope is given by the formula: ∆y∆x, where Δy is the change in position and Δx is the change in time. Choose two points on the tangent line and compute the slope using this formula.
Step 5: Interpret the slope value. The slope of the tangent line at t = 30s gives the velocity of the bicycle at that specific time. Ensure the units are consistent (e.g., meters per second) and reflect the physical meaning of the graph.

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Key Concepts

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

Position vs. Time Graph

A position vs. time graph visually represents an object's position over time. The x-axis typically denotes time, while the y-axis shows position. The slope of the graph at any point indicates the object's velocity, with a steeper slope corresponding to a higher velocity.
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Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both speed and direction. In the context of a position vs. time graph, velocity can be determined by calculating the slope of the graph at a specific time point.
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Calculating Slope

The slope of a line on a graph is calculated by taking the change in the y-values divided by the change in the x-values (rise over run). For a position vs. time graph, this calculation gives the velocity of the object. At t = 30s, identifying the coordinates of the graph at that time allows for the determination of the slope and thus the velocity.
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Related Practice
Textbook Question

Larry leaves home at 9:05 and runs at constant speed to the lamppost seen in FIGURE EX2.1. He reaches the lamppost at 9:07, immediately turns, and runs to the tree. Larry arrives at the tree at 9:10. What is Larry's average velocity for the entire run?

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Textbook Question

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 40 mph and half the distance at 60 mph. On her return trip, she drives half the time at 40 mph and half the time at 60 mph. What is Julie's average speed on the way to Grandmother's house?

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Textbook Question

FIGURE EX2.4 is the position-versus-time graph of a bicycle. What is the bicycle's velocity at t = 5s

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Textbook Question

FIGURE EX2.5 shows the position graph of a particle. Draw the particle’s velocity graph for the interval .

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Textbook Question

A particle starts from at and moves with the velocity graph shown in FIGURE EX2.6. Does this particle have a turning point? If so, at what time?

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Textbook Question

A particle starts from x0 = 10 m at t0 = 0 s and moves with the velocity graph shown in FIGURE EX2.6. What is the object’s position at t = 2 s and 4 s?

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