Representing motion

Chapter 2: Representing

Motion

How will you know that something is

moving?

Is the car moving? What about the trees and the couple standing?

Defend your answers.

All Kinds of Motion• When an object is in motion, its

position changes.• Its position can change in many ways,

including– straight line– a circle– back-and-forth vibration

Picturing MotionCopyright © McGraw-Hill Education

All Kinds of Motion• A description of motion relates to

place and time.• Give and describe several examples of

motion from your own experience.


Motion Diagrams and Particle Models

• A series of images showing the positions of a moving object at equal time intervals is called a motion diagram.

• In a particle model, you replace the object or objects of interest with single points.


Motion Diagrams and Particle Models


Concepts in Motion (video)

Ticker tape Analysis

Ticker tape analysis activity

Renatta’s movement starts from a high speed to low speed until she finally stopped. She remains at rest for a while and then slowly moves and goes faster again until the trace ends.

Renatta travels at a constant speed during the first time interval and then gradually moves faster until the trace ends


Renatta moves with a constant speed in the first time interval. She then abruptly slows down to a stop. She remains at rest for sometime and then moves with a constant speed, slower than the first speed.


Renatta moves with a constant slow speed in the first time interval, then she moves a little bit faster then slows down in the second time interval and then slowly moves again at a constant pace and speeds up in the third time interval.


Renatta’s movement slows down in the first interval then becomes slower in a constant motion in the second time interval. It speeds up and slows down again in the third time interval. Then she constantly moves in a very slow pace in the fourth time interval.

Further reinforcement on Particle Model construction and

analysis

MOTION AND PARTICLE DIAGRAM ACTIVITY

• How does a motion diagram represent an object’s motion?

a symbolical representation of an object in motion.• Draw a particle model motion diagram for a path. bike

rider moving at a constant pace along a straight

. . . . . . . . . .


• Draw a particle model motion diagram corresponding to the motion diagram in Figure 4 for a car coming to a stop at a stop sign. What point of the car did you use to represent the car?


• Draw a particle model motion diagram corresponding to the motion diagram in Figure 5 for a flying bird. What point on the birds did you choose to represent the bird?


• Draw a particle model motion diagrams for two runners during a race in which the first runner crosses the finish line as the other runner is three-fourths of the way to the finish line.

. . . . . . .

. . . . . . . . .


Starts with constant slow speed, then moves a little bit faster then slows down and then slowly moves again at a constant pace and speeds up.


At first it slows down then becomes even slower in a constant motion, later on it speeds up and slows down again then shifted to a constant very slow pace.

Coordinates System

Coordinate Systems• A coordinate system tells you the location

of the zero point of the variable you are studying and the direction in which the values of the variable increase.

• The origin is the point at which both variables have the value zero.

Where and When?Copyright © McGraw-Hill Education

Coordinate Systems• Consider a runner on this coordinate system.• You can indicate how far away an object is from the

origin at a particular time by drawing an arrow from the origin to the object.

• The two arrows locate the runner’s position at two different times.

• Position is the distance and direction from the origin to the object.


Vectors and Scalars• Quantities that have both size (also

called magnitude) and direction are called vectors.

• Vectors can be represented by arrows.– Position is an example of a vector. It

is represented by the symbol x.


x1 x2

Vectors and Scalars• A quantity that is just a number without any direction

is a scalar.

• Examples of scalars:– Time

– Distance

– Temperature

• Is mass a scalar? Explain.– Yes. Mass has a magnitude, but no direction.


Vectors and Scalars• The difference between two times is called a time

interval.

• Time intervals are scalars.

• The time interval is defined mathematically as follows:

• ∆ is the Greek letter delta. It is used to represent a change in a quantity.


Vectors and Scalars• A change in position is called a displacement.

• Displacement is a vector. It is drawn with its tail at the earlier position and its tip at the later position.

• Displacement can be represented mathematically as


∆x = xf − xi

∆x

xfxi

Vectors and Scalars• A vector that represents the sum of two other vectors is

called a resultant.

• Example of Vector Addition


Vectors and Scalars• Example of Vector Subtraction


Vectors and Scalars• Example of Vector Subtraction


Activity: Vector Addition & Subtraction

Activity Results1. Two vectors of the same magnitude are added; one pointing east, one west. The magnitude of the resultant vector is

Answer: 0

Activity Results2. A boat moves 10 km due west, 5 km due east, and then 10 km due west. The displacement of the boat from its initial position is(-10km) + (5km) + (-10km) = -15km

Activity Results3. What is the magnitude of your displacement when you follow directions that tell you to walk 150 m north, then 25 m south?

(150m) + (-25m) = 125m

Activity Results4. A car drives from city A to city B in 52 minutes. If the car arrives at city B on 2:36 PM, what time did it leave city A?

2:36 - 52 = 1:44pm

Activity Results

5. In the diagram below, what is the time interval of an object going from position B to position D?

T = tf – ti 40s – 10s = 30s

POSITION TIME GRAPH

POSITION-TIME GRAPH

• Motion diagrams can illustrate the movement of objects, tables and graphs can also do the same.

• Position - time graph is a graph with time data plotted on x-axis and position data on y-axis.

INSTANTANEOUS POSITION• position at a particular instant

• Make a position time graph of the runner’s motion below

• CRITICAL THINKING: Why is the line on the graph sloped even though it describes a motion along a straight path?

Velocity vs. SpeedWhat is the difference between speed and velocity? - Speed is the value of distance covered by an object at a certain amount of time. - velocity is speed with direction

What can you describe about this two joggers?

How can you prove which is the faster jogger?

Velocity computation:

or V = d/t

Take note…

Example: • 50m / 5s = 10m/s• 50m / 10s = 5m/s

When ΔX gets larger, the speed gets larger; when Δt gets larger, the speed gets smaller.

Other points to take note…• An upward slope above the x-axis means the velocity

is positive, and the object is moving away from the origin.

• An upward slope below the x-axis means the velocity is positive, and the object is moving towards the origin

• A downward slope above the x-axis means the velocity is negative, and the object is moving towards the origin.

• A downward slope below the x-axis means the velocity is negative, and the object is moving away the origin

Other points to take note…

Challenge Question:• Is it possible to have an accurate position-

time graph that is a vertical line? What about a horizontal line?

• Vertical line – No, because it is impossible for an object moving to increase its distance without increasing its time.

• Horizontal line – Yes, because this means that the object is not moving but the time can continuously increase.

DID YOU KNOW?1. What is the fastest land animal? Cheetah has a recorded speed of 109.4–120.7 km/h (68.0–75.0 mph)2. What is the fastest flying animal?- Peregrine falcon has a recorded speed of 389 km/h (242 mph)

DID YOU KNOW?3. What is the fastest recorded 100-m dash?- The current men's world record is 9.58 seconds, set by Jamaica's Usain Bolt in 2009, while the women's world record of 10.49 seconds set by American Florence Griffith-Joyner in 1988 remains unbroken.

DID YOU KNOW?4. What is the fastest possible speed in the universe?- the speed of light = 299 792 458 m / s

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Science

Representing motion