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Chapter 1

Lecture Presentation

Representing Motion

Lecture Presentation

© 2015 Pearson Education, Inc. Slide 1-2

Chapter 1 Representing Motion

Chapter Goal: To introduce the fundamental concepts of motion and to review related basic mathematical principles.

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Pre-Lecture Video“ Introduction ”

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Types of Motion

• Motion is the change of an object’s position or orientation with time.

• The path along which an object moves is called the object’s trajectory .

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Making a Motion Diagram

• A composite image showing objects position at several equally spaced instants of time. (type of video analysis)

• These motion diagrams in one dimension show objects moving at *constant speed, *speeding up, and *slowing down.

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Making a Motion Diagram

• This motion diagram shows motion in two dimensions with changes in both speed and direction.

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Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower?

Car A Car B

QuickCheck 1.1

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The Particle Model

• The particle model of motion is a simplification in which we treat a moving object as if all of its mass were concentrated at a single point.

• Commonly used to simplify video analysis.

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QuickCheck 1.2

Two runners jog along a track. The positions are shown at 1 s intervals. Which runner is moving faster?

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QuickCheck 1.3

Two runners jog along a track. The times at each position are shown. Which runner is moving faster?

A. Runner AB. Runner BC. Both runners are moving at the same speed.

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Time

• For a complete motion diagram we need to label each frame with its corresponding time (symbol t) as read off a clock.

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Change in Time

• In order to quantify motion, we’ll need to consider changes in time, which we call time intervals.

• A time interval ∆t measures the elapsed time as an object moves from an initial position xi at time ti to a final position xf at time tf. ∆t is always positive.

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Position and Coordinate Systems

• To specify position we need a reference point (the origin ), a distancefrom the origin, and a direction from the origin.

• The combination of an origin and an axismarked in both the positive and negative directions makes a coordinate system. (recall vectors and the Cartesian plane)

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Position and Coordinate Systems

• The symbol that represents a position along an axis is called a coordinate. (position is often represented with a symbol such as “x” or “y”)

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Example Problem

Jane walks to the right at a constant rate, moving 3 m in 3 s. At t = 0 s she passes the x = 1 m mark. Draw her motion diagram from t = –1 s to t = 4 s.

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Changes in Position and Displacement

• A change of position is called a displacement.

• Displacement is the difference between a final position and an initial position and is a signed quantity.

∆x = x2 – x1 = 0 ft – 50 ft = -50 ft OR 50 ft west

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Displacement Vectors

• The displacement vector represents the distance and direction of an object’s motion from the starting position.

• An object’s displacement vector is drawn from the object’s initial position to its final position, regardless of the actual path followed between these two points. The sum of actual path followed is the distancetraveled .

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QuickCheck 1.4

Maria is at position x = 23 m. She then undergoes a displacement ∆x = –50 m. What is her final position?

A. –27 mB. –50 mC. 23 mD. 73 m

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QuickCheck 1.5

An ant zig-zags back and forth on a picnic table as shown.

The ant’s distance traveledand displacementareA. 55 cm and 55 cmB. 30 cm and 55 cmC. 55 cm and 30 cmD. 55 cm and –55 cmE. 50 cm and –30 cm

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Velocity and Speed

• Motion at a constant speed in a straight line is called uniform motion .

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Velocity and Speed

• When traveling in a straight line, speed measures only how fast an object moves, but velocity tells us both an object’s speed and its direction.

• Bikes have same speed but not same velocity – why?

• The velocity defined by Equation 1.2 is called the averagevelocity.

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Velocity Vectors

• We represent the velocity of an object by a velocity vector that points in the direction of the object’s motion, and whose magnitude is the object’s speed.

The motion diagram for a car starting from rest

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QuickCheck 1.5

An ant zig-zags back and forth for 10 seconds on a picnic table as shown.

The ant’s speed and velocity areA. 5.5 cm/s and 5.5 cm/sB. 3.0 cm/s and 5.5 cm/sC. 5.5 cm/s and 3.0 cm/sD. 5.5 cm/s and –5.5 cm/sE. 5 cm/s and –3 cm/s

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Example Problems

1. Frank is walking East, at t = 12 s, Frank is at x = 25 m. 5 s later, he’s at x = 20 m. What is Frank’s velocity?

(Remember to Prepare, Solve and Assess)

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Chapter 1 Homework Assignment

MasteringPhysics “”Ch 1 HW”

ORFrom Text: Q: 3, 13 and P: 2, 7, 8, 25, 39, 57

(you must show work for on-line or book work)

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