1. Representing Motion
Chapter 2

2. 2.1 Picturing Motion What kinds of motion can you describe?
How do you know that an object has moved? Be specific.
Let’s start at the very beginning… Straight Line Motion.

3. Motion Diagrams
A series of images showing the positions of a moving object at equal time intervals is called a motion diagram.
A particle model is a simplified version of a motion diagram in which the object in motion is replaced by a series of single points.

4. 2.2 Where and When? Beginning Vectors
Coordinate Systems
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 a value of zero
Position can be represented by drawing an arrow from the origin to the point representing the object’s new location
The length of the arrow indicates how far the object is from the origin or the distance.

5. Vectors and Scalars Vectors Scalars
Have magnitude (size) and direction
Require the use of VECTOR ADDITION to determine resultant vector
Only have magnitude
Can be added or combined using standard rules of addition and subtraction
Vector
Scalar
Displacement
Distance
Velocity
Speed
Acceleration
Time
Force
Temperature

6. Vector Addition (Graphical Method)
You will need a ruler, protractor, and pencil
Draw a coordinate system (small) as your origin
Draw an arrow with the tail at the origin and the head pointing in the direction of motion.
The length of the arrow should represent the distance traveled.
Add the second vector using the head to tail method.
Measure resultant magnitude and direction.

7. Vector Addition (Geometry and Trig)
Add vectors using “head to tail” method.
Pictures do not need to be drawn to scale. No need for a ruler and protractor.
Use Pythagorean Theorem and SOHCAHTOA to solve for resultant vectors ONLY when RIGHT TRIANGLES are formed.
If not right triangles, use Law of Sines and Law of Cosines to solve for resultant vectors.

8. Time Intervals and Displacements
The difference between two times is called a time interval and is expressed as
i and f can be any two time variables you choose (according to each problem)
A change in position is referred to as displacement.

9. Displacement Ins and Outs
Distance ≠ Displacement
Displacement is the shortest distance from start to finish or “as the crow flies”
Draw the following:
10m East
-10m
10m North + 12m West

10. Vector Components Every vector has x- and y- components.
In other words, a vector pointing southwest has both a south (y) and west (x) component.
Vectors can be “resolved into c0mponents”.
Use SOHCAHTOA to find the x- and y- components

11. Vector Addition (x- y- Component Method)
Break EACH vector into x- and y- components.
Assign negative and positive values to each component according to quadrant rules. For instance, south would have a negative sign.
Add the x- column. Add the y- column.
Use Pythagorean Theorem to determine the final displacement magnitude.
Use SOHCAHTOA to find the final displacement direction.

12. 2.3 Position – Time Graphs
Plot time on the x-axis and position on the y-axis
Slope will indicate average velocity
Use this website for extra help.
Shape of Slope
Interpretation
Linear
Constant speed
(can be positive or negative)
Parabolic
Speeding up
Hyperbola
Slowing down

13. Position - Time Graphs
By plotting the time (t) and position (d) data of a particular object a position-time graph can be generated.
Remember that d represents that object’s instantaneous position.
t d
30 0
55 0

14. 2.4 How Fast?
Average velocity is defined as the change in position, divided by the time during which the change occurred.
On a position vs. time graph, both magnitude and relative direction of displacement are given. A negative slope indicates an object moving toward the zero position.
Speed simply indicates magnitude or “how fast.”
Velocity indicates BOTH magnitude and direction. In other words velocity tells you “how fast” and “where.”

15. Average Velocity
Defined as the change in position divided by the time during which the change occurred.
v = ∆d / ∆t = df - di / tf - ti
Average velocity is represented by the slope of the line in a position-time graph

16. Instantaneous Velocity
When solving for average velocity, two points for position and time are chosen for comparison. Individual changes in speed could have taken place within those intervals.
Instantaneous velocity represents the speed and direction of an object at a particular instant.
On a position-time graph, instantaneous velocity can be found by determining the slope of a tangent line on the curve at an given instant.

17. Speed vs. Velocity
Speed is how fast an object in moving. It is a scalar quantity and therefore can never be negative.
Velocity is speed with direction. It is a vector quantity and therefore can be negative.
Instantaneous velocity is the speed and direction of an object at a particular instant.

18. Expressing Motion in Terms of An Equation
So far, we have looked at motion diagrams, particle models, and graphs as a means of representing motion.
Equations are also quite useful.
Based on the equation y=mx +b, one final equation will be derived in this chapter.
d = final position
v = average velocity
t = time interval
di = initial position (based on y-intercept if using a graph)

19. Final Thoughts
Read Chapter 1! You will reinforce all of these concepts, drill them into your head and see more examples than I have given here.
Visit This website offers great explanations of physics concepts.
Watch this video. It is a little boring but very helpful.