Chapter 2. One Dimension Motion 2.1 Motion diagram 2.2 Distance and Displacement 2.1 Motion diagram 2.2 Distance and Displacement.

Chapter 2. One Dimension Chapter 2. One Dimension MotionMotion

2.1 Motion diagram2.1 Motion diagram

2.2 Distance and 2.2 Distance and DisplacementDisplacement

2.1 Motion diagram2.1 Motion diagram

2.2 Distance and 2.2 Distance and DisplacementDisplacement

Objectives: You are able toObjectives: You are able to

• Draw Draw motion diagram motion diagram and describe motion.and describe motion.

• Understand a concept of Understand a concept of particle modelparticle model to to present a moving object. present a moving object.

• Demonstrate your understanding of Demonstrate your understanding of vector vector and scalar quantity and scalar quantity and difference between and difference between distance and displacement.distance and displacement.

• Show understanding of directions and signs Show understanding of directions and signs for displacement.for displacement.

Uniform motion Uniform motion in One Dimension:in One Dimension:

• Motion is along a straight line Motion is along a straight line (horizontal, vertical or slanted).(horizontal, vertical or slanted).

• The moving object is treated as though The moving object is treated as though it were a point particle.it were a point particle.

Describing MotionDescribing Motion

The study of one-dimensional kinematics is concerned with the multiple means by which the motion of objects can be represented. Such means include the use of words, graphs, equations, and diagrams.

Motion diagramMotion diagram

A series of images showing the A series of images showing the positions of a moving object at positions of a moving object at equal time intervals.equal time intervals.

Particle modelParticle model

• A simplified version of a motion A simplified version of a motion diagram in which the object in diagram in which the object in motion is replaced by series of motion is replaced by series of single points. single points.

• To use the particle model, the size To use the particle model, the size of the object must be much less of the object must be much less than the distance it moves. than the distance it moves.

Practice ProblemsPractice Problems 1. Use the particle model to draw a 1. Use the particle model to draw a motion diagram for a bike rider riding at motion diagram for a bike rider riding at constant pace. constant pace.

2. Draw a constant motion diagram with 2. Draw a constant motion diagram with seven dots. If it presents 12 s, how much seven dots. If it presents 12 s, how much time passed between adjacent dots.time passed between adjacent dots.

3. Page 33, # 3 and 43. Page 33, # 3 and 4

2.2 Where and When?2.2 Where and When?

Coordinate system:Coordinate system:

-OriginOrigin

-Measurable straight line with Measurable straight line with numbersnumbers

A one-dimensional A one-dimensional coordinate systemcoordinate system• You are free to choose the origin You are free to choose the origin

and positive direction as you like, and positive direction as you like, but once your choice is made, stick but once your choice is made, stick with it.with it.

Vector and ScalarVector and Scalar

• Vector – quantities have magnitude Vector – quantities have magnitude and directionand direction

• Scalar – quantities have only Scalar – quantities have only magnitude magnitude

Distance and Distance and DisplacementDisplacement

Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below:

Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below:

A

Bs = 20 m

DistanceDistance ss is a is a scalarscalar quantity (no quantity (no direction):direction):Contains Contains magnitudemagnitude only and consists of a only and consists of a numbernumber and a and a unit.unit.

(20 m, 40 mi/h, 10 (20 m, 40 mi/h, 10 gal)gal)

Distance and Distance and DisplacementDisplacement

DisplacementDisplacement is the straight-line separation is the straight-line separation of two points in a specified direction.of two points in a specified direction.DisplacementDisplacement is the straight-line separation is the straight-line separation of two points in a specified direction.of two points in a specified direction.

A vector quantity:

Contains magnitude AND direction, a number, unit & angle.

(12 m, 300; 8 km/h, N)

A

BD = 12 m, 20o

Distance and Distance and DisplacementDisplacement

• For motion along x or y axis, the For motion along x or y axis, the displacementdisplacement is determined by the x or y coordinate of its is determined by the x or y coordinate of its final position. Example: Consider a car that final position. Example: Consider a car that travels 8 m, E then 12 m, W.travels 8 m, E then 12 m, W.

• For motion along x or y axis, the For motion along x or y axis, the displacementdisplacement is determined by the x or y coordinate of its is determined by the x or y coordinate of its final position. Example: Consider a car that final position. Example: Consider a car that travels 8 m, E then 12 m, W.travels 8 m, E then 12 m, W.

Net displacement Net displacement DD is from the origin to is from the origin to the final position:the final position:

What is the What is the distancedistance traveled? traveled?20 m !!

12 m,W

D

D = 4 m, WD = 4 m, W

x8 m,E

x = +8

x = -4

The Signs of DisplacementThe Signs of Displacement• Displacement is positive (+) or Displacement is positive (+) or

negative (-) based on negative (-) based on LOCATIONLOCATION..

2 m

-1 m

-2 m

The displacement is the y-coordinate. Whether motion is up or down, + or - is based on LOCATION.

Examples:

The direction of motion does not matter!The direction of motion does not matter!

Practice problemsPractice problems• What is distance and displacement What is distance and displacement

after 4 sec.after 4 sec.

• Page 37, # 7 and 8Page 37, # 7 and 8