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

Knight Calc 5th Edition

Ch 02: Kinematics in One Dimension

Problem 4a

Chapter 2, Problem 4a

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

Verified step by step guidance

Step 1: Understand the problem. The velocity of the bicycle at a specific time can be determined from the slope of the position-versus-time graph at that time. Velocity is the rate of change of position with respect to time.

Step 2: Recall the formula for velocity from a position-time graph: \( v = \frac{\Delta x}{\Delta t} \), where \( \Delta x \) is the change in position and \( \Delta t \) is the change in time. The slope of the graph at a given point represents the instantaneous velocity.

Step 3: Locate \( t = 5 \, \text{s} \) on the graph. Identify the segment of the graph that corresponds to this time and determine whether the graph is linear or curved at this point.

Step 4: If the graph is linear at \( t = 5 \, \text{s} \), calculate the slope of the line by selecting two points on the line near \( t = 5 \, \text{s} \). Use the formula \( \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \), where \( y \) represents position and \( x \) represents time.

Step 5: If the graph is curved at \( t = 5 \, \text{s} \), draw a tangent line to the curve at \( t = 5 \, \text{s} \). Calculate the slope of this tangent line using the same formula \( \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \). This slope represents the instantaneous velocity at \( t = 5 \, \text{s} \).

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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 represents time, while the y-axis represents position. The slope of the graph at any point indicates the object's velocity, with a steeper slope corresponding to a higher velocity.

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 tangent line at a specific point on the graph.

Tangent Line

A tangent line is a straight line that touches a curve at a single point without crossing it. In the context of a position vs. time graph, the slope of the tangent line at a given time indicates the instantaneous velocity of the object at that moment. This is crucial for determining how fast the bicycle is moving at t = 5s.

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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

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

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

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, in, during each of these two intervals?

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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