1. Physics chapter 2 Ms. Pollock
Representing Motion
Physics chapter 2
Ms. Pollock

2. 2.1 Picturing Motion
Using measurement and calculation to analyze motion
Allow determination of how fast and how far an object will move
Perception of motion instinctive – eyes naturally notice moving objects more than stationary ones
large.jpg

3. All Kinds of Motion
Motion = change in position along path of straight line, circle, arc, or back-and-forth
Study begun with motion along straight line – simplest motion
Motion related to space and time

4. Motion Diagrams
Series of intervals showing location of object at regular time intervals
Everything in background in same position
Only object being observed in motion

5. The Particle Model
Tracking motion easier if following single point on object
Particle motion simplified version of motion diagram
Size of object must be smaller than size of motion
ak0.pinimg.com/736x/86/7f/82/867f82d4e3fc19096e542a92cc083d74.jpg

6. 2.2 Where and When?
Measurements of motion possible with addition of standard measuring devices
Important to set coordinates for reference
a2f2f c6f e6c d6f74696f6e2e636f6d2f646f63756d656 e f6e2f696d f4c f e706e67

7. Coordinate Systems
Coordinate system – location of zero point of variable being studied and direction in which values of variable increase
Origin – point at which both variables have zero value
Arrows representing position
system.svg.png/ /250px-Cartesian-coordinate-system.svg.png

8. Coordinate Systems Position – separation between object and origin
Length of arrow indicates distance
Negative position possible, if measurement to left of origin
egativeDisplacement.png

9. Vectors and Scalars Magnitude – size
Vector – quantity with both magnitude and direction
Scalar – quantity without direction
Vector represented in boldface and scalar represented in regular type in this text

10. Vectors and Scalars Familiar with scalar addition
Vectors altered by direction and unit
Example p. 35
Resultant – sum of vectors; always points from tail of first vector to tip of last vector

11. Time Intervals and Displacements
Time interval – difference between two times; t = tf – ti
Position – vector with tail at origin of coordinate system and tip at place
Displacement – change in position; d = df – di
Initial and final at beginning and end of any chosen interval
Complete description of displacement require distance traveled and direction moved
displacement.png

12. Time Intervals and Displacements
Distance and displacement not the same; distance scalar, displacement vector
Displacement same in any coordinate system
Displacement often used in study of motion
.png

13. 2.3 Position-Time Graphs
Often helpful to represent motion in different ways
Helpful in determining displacement
Graphs often helpful in organizing information
age3/files/page3_1.jpg

14. Using a Graph to Find Out Where and When
Position-time graph – line graph with time data on horizontal axis and position data on vertical axis
Graph not picture of object’s path– picture of object’s speed
Can be used to estimate position beyond what is known

15. Example Problem 1
When did the runner whose motion is described in Figure 2-12 reach 30.0 m beyond the starting point? Where was he after 4.5 s?

16. Practice Problems
P. 39 #

17. Position vs. Time
Instantaneous position – position of object at particular point in time, represented by d
Representations of motion equivalent – important to learn which are best for solving different kinds of problems
Can also be done for multiple objects f

18. Challenge Problem
Niram, Oliver, and Phil all enjoy exercising and often go to a path along the river for this purpose. Niram bicycles at a very consistent km/h, Oliver runs south at a constant speed of 16.0 km/h, and Phil walks south at a brisk 6.5 km/h. Niram starts biking north at noon from the waterfalls. Oliver and Phil both start at 11:30 AM at the canoe dock, 20.0 km north of the falls.
1. Draw position-time graphs for each person.
2. At what time will the three exercise enthusiasts be within the smallest distance interval?
3. What is the length of that distance interval?

19. Example Problem 2
When and where does runner B pass runner A?

20. Practice Problems
P. 41 #

21. 2.4 How Fast?
Displacement and time needed to show how fast an object is moving
Recall slope calculation (rise over run)
With distance and time, velocity (slope) can be calculated.
Red slope = (6.0 m – 2.0 m) / (3.0 s – 1.0 s) = 2.0 m/s
Blue slope = (3.0 m – 2.0 m) / (3.0 s – 2.0 s) = 1.0 m/s

22. Average Velocity Change of position related to time interval
v = d / t = (df – di) / (tf – ti)
Slope of position time graph not speed, but velocity – has magnitude and direction

23. Average Speed Absolute value of position-time graph slope
Speed – how fast object is moving
Sign of slope direction of motion
speed-graph-bus-journey.png

24. Example Problem 3
The graph at the right describe the motion of a student riding his skateboard along a smooth, pedestrian-free sidewalk. What is his average velocity? What is his average speed?
v = d/t = (df – di) / (tf – ti)
v = (12.0 m – 6.0 m) / (8.0 s – 4.0 s)
v = 6m / 4 s
V = 1.5 m/s in positive direction

25. Practice Problems
P. 45 #

26. Instantaneous Velocity
Average velocity describing what happened at several different times during the motion of the object
Instantaneous velocity – speed at specific time within motion of object
May indicate stop or change in direction

27. Average Velocity on Motion Diagrams
Vectors related to magnitudes of motions
Average velocity equation of motion
d = vt – di
Direction specified by positive and negative charge