1. Physics Chapter 2
Representing Motion

2. Standards
1.Newton's laws predict the motion of most objects. As a basis for understanding this concept:
a. Students know how to solve problems that involve constant speed and average speed.

3. Agenda Turn in Chapter 1 Homework, Worksheet, & Lab Lecture & Practice
Q&A

4. Motion Kinematics: Study of motion, emphasizing on describing motion
Motions in nature, such as falling leaves, are in general very complicated for us to analyze at this point, so we start with simple, often hypothetical, motions.
Simplest motion:
1-Dimensional
Point Particle: no rotation

5. Position Position: Location, where an object is
Symbol: d (Most often, x)
Unit: meter (m)
How to describe a position in 1-D?
Frame of Reference (numbered line)
Reference point: origin
Direction:
Positive direction: We can define the positive direction to be any direction we want, normally direction of motion
Negative direction: Opposite to positive direction

6. Position is a vector:
Direction: negative sign indicates direction only (more on Ch 5)
Magnitude: how far from the origin

7. Position and Frame of Reference
10 miles
West
Hami
Downtown, LA
East
Frame 1: Define East positive, and d = 0 at Downtown LA, then position of Hami is _____ miles.  
Frame 2: Define West positive, and d = 0 at Downtown LA, then position of Hami is _____ miles.
Frame 3: Define East positive, and d = 0 at Hami, then position of Hami is _____ miles. 
-10
(- indicates only direction, west.)
+10

8. So, Representing Position …
The representation of a position depends on the choice of the frame of reference.
The same position can be expressed in different ways in different frame of reference.
But the physical meaning of position does not change, regardless the choice of frame of reference.
Hami still is 10 miles west of Downtown LA, no more or less.
If you want to go from Downtown LA to Hami, you still have to go 10 miles west.

9. Displacement + Displacement: Change of position
Symbol: d (most often x, Δ = change)
d = d2 - d1 = df - di
Displacement is also a vector:
Magnitude: how far
Direction: Negative sign indicates direction only, it has nothing to do with magnitude.
larger than
A –3m displacement is ___________ a 2m displacement.
Unit: same as position, meter
Displacement has nothing to do with the actual path. It depends only on the initial and final positions.

10. Distance (D) Distance  Displacement
Distance is equal to Magnitude of Displacement when there is no change in direction.
D = |d|
Distance is a scalar. (magnitude only)
Total distance is not necessarily equal to the magnitude of total displacement.
Displacement cares only end points; distance cares both end points and the actual path.
Position and displacement depend on frame of reference; yet distance does not depend on frame of reference.

11. Total Distance
Whenever there is a change in direction, total distance will not be the same as the magnitude of total displacement.
When you go from d = 0 to 3m then back to 2m,
Your total displacement is __ m.
Your total distance traveled is __ m. 2 4

12. Total Distance When there is no change in direction:
When there is change in direction:
where D1 and D2 are distances of segments in which there is no change in direction.

13. Average Velocity
Average velocity: ratio of displacement d that occurs during a particular time interval t to that time interval
Standard Unit: m/s

14. Average speed
Average speed is total distance traveled during a time interval divided by that time interval.
Standard Unit: m/s

15. Example 1: A high school athlete runs 1. 00  102 m in 12. 20 s
Example 1: A high school athlete runs 1.00  102 m in s. What is the velocity in m/s and km/h?
Given: d = 1.00  102 m, t = 12.20s
Unknown: v = ?

16. Practice 1: A person walks 13 km in 2. 0 h
Practice 1: A person walks 13 km in 2.0 h. What is the person’s average velocity in km/h and m/s?
Given: d=13km, t=2.0h

17. Constant Velocity
Then

18. Example 2: At 1:00 PM, a car, traveling at a constant velocity of 94 km/h toward the west, is 17 km to the west of your school. Where will it be at 3:30 PM?
Define west to be the positive direction. Let d = 0 at school.
ti = 1 h, tf = 3.5 h, di = 17 km, v = 94 km/h, df = ?
Final position is 252 km west of school.

19. Example 2: At 1:00 PM, a car, traveling at a constant velocity of 94 km/h toward the west, is 17 km to the west of your school. Where will it be at 3:30 PM?
Define west to be the positive direction. Let d = 0 at school.
ti = 1 h, tf = 3.5 h, di = 17 km, v = 94 km/h, df = ?
v: km/h
d: km
t: h
Double check units.
Final position is 252 km west of school.

20. Problem Solving Strategy
Set up Frame of Reference
Write down given and unknown
Write down useful equation
Manipulation equation to express unknown as a function of other givens
Plug in numbers and get result
Answer question in physical terms if needed

21. What happens to the average velocity when t becomes very small?
When the time interval becomes very, very small, like s, the average velocity essentially becomes the velocity at that moment.
 Instantaneous velocity: the velocity at a single moment.

22. Instantaneous velocity
What does the slope of this line mean? d t
Tangent line
Slope = average velocity from time ti to t1 t4 ti t3 t2 t1
As the time interval becomes smaller and smaller, average velocity becomes instantaneous velocity, which is the slope of the tangent line.

23. Instantaneous Velocity and Slope
On a position (versus time) graph, we can find the instantaneous velocity at any time by finding the slope of the line tangent to the curve at that time.
If graph is a straight line:
slope is _________, and
constant
_________ is constant.
velocity

24. Speed Instantaneous speed is magnitude of instantaneous velocity.
Average speed is not necessarily equal to magnitude of average velocity.

25. d
Describe in words the motion of the four walkers shown in the four curves. Assume the positive direction is east and the reference point is the corner of High Street. A B t D C
A: starts from the corner of High St. and moves toward east at constant speed.
Practice:
B: starts from _________the corner of High St. and moves toward _____ at a ______________ speed.
west of
east
slower constant
C: starts from _____ corner of High St. and moves toward ______ with __________ speed.
at the
west
decReasing
D: starts from _____ of the corner of High St. and moves toward _____ at ________ speed.
east
west
constant

26. Practice 3: Sketch position-time graphs for these four motions: a
Practice 3: Sketch position-time graphs for these four motions: a. starting at a positive position with a positive velocity. b. starting at a negative position with a smaller positive velocity. c. remaining at a negative position. d. starting at a positive position with a negative velocity. d a b t c d

27. Given: ti = 0, tf = 30 min, di = 0, df = 20 km
45-27: The graph in Fig represents the motion of a bicycle. Determine the bicycle’s average speed and average velocity, and describe its motion in words.
position (km) 20
t (min) 30
Given: ti = 0, tf = 30 min, di = 0, df = 20 km
in the positive direction.
The bicycle starts from the reference point at time 0 and moves in the positive direction with a constant speed of 0.67 km/min.

28. 45-28: When Marilyn takes her pet dog for a walk, the dog walks at a very consistent pace of 0.55 m/s. Draw a motion diagram and position-time graph to represent Marilyn’s dog walking the 19.8-m distance from in front of her house to the nearest fire hydrant. +
19.8m
d (m)
19.8
t (s) 36

29. Practice 5: Sketch velocity-time graphs for the graphs in the figure.d c c b b a a t t

30. D0  8s = __________________
AI + AII
> 0
Velocity vs. Time Graph
The area under the curve of v-t graph from ti to tf is the displacement from time ti to tf.
Positive, negative, or 0 v
(m/s) AI
t (s) 5
AII 8 AI
d05s = __________________
> 0
-AII
d58s = __________________
< 0
AI - AII
Could be < 0 if AI < AII
d0  8s = __________________
> 0

31. Example 4: A car moves along a straight road at a constant velocity of +75 km/h for 4.0 h, stops for 2.0 h, and then drives in the reverse direction at the original speed for 3.0 h. a. Plot a velocity-time graph for the car. b. Find the area under the curve for the first 4 h. What does this represent? c. Explain how to use the graph to find the distance the car is from its starting point at the end of 9.0h. a. b.
v (km/h) 75 AI
It represents the displacement in the first 4 hours.
t (h) 1
AII c.
AI + AII
-75

32. Lightyear
= distance traveled by light in one year

33. WS APK-6 A B +
Let’s assume the time for B to catch up is Δt, then distance A runs is
Similarly, distance run by B is