1. Introduction to
Motion
Chapter 2

2. Coordinate Systems
 Describing motion requires a frame of reference called a
coordinate system
 One dimension:
 Two dimensions:

3. “Position”
 As an object moves, its position changes
 We normally define movement to the right as “positive” and
movement to the left as “negative”

4. “Distance”
 Distance is the length of the path traveled
 Distance has no direction. It is always positive.
 Calculate distance traveled…

5. “Displacement”
 Displacement is the overall change in position
∆𝑥 = 𝑥 𝑓 − 𝑥𝑖
 It can also be defined as the “length of a line between the
starting and ending points.
 Displacement is a vector quantity, which can be positive or
negative
 Distance and displacement may be the same or may not
be!

6. Distance vs. Displacement
 Calculate distance. Calculate displacement.
1. A train travels in a straight line 162 miles from Phoenix to Yuma.
2. A student walks down the hallway from the Physics classroom to
the music classroom, then back to the math classroom.
3. A boy walks two miles to school, then later walks those two miles
home.

7. Distance vs. Displacement
4. Skier skis 180 meters east, then 140 meters west, then 100
meters east.
5. A kiddy roller coaster travels at 6 m/s around a circular track
for 15 seconds, then returns back to the station.

8. Average Speed
 Speed is “rate of motion”
 Average speed is distance traveled over a given amount of
time
 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒
 Units for speed are m/s

10. Examples
1. Suppose the kingfisher from the previous problem dives with an
average speed of 4.6 m/s for 1.4 s before hitting the water. What
was the height from which the bird dove?
2. If you hear a flash of lightning, then thunder 3.5 s later, how far
away from you did the lightning bolt strike? (The speed of sound
is 340 m/s.)
3. A kangaroo can hop at speeds up to 65 km/h.
 How much time will it take the kangaroo to hop 0.25 km at this speed?
 How far (m) can a red kangaroo hop in 3.2 minutes at this speed?

14. Challenge Problem
 A girl rides quickly down the hill on her bike at a
speed 11 m/s. She reaches the bottom of the hill in
1.2 minutes, then immediately turns around and
pedals back uphill at a speed of 3 m/s. If it takes her
3.5 minutes to bike back to the top of the hill, what
was the girl’s average speed over the entire time?

15. Average Velocity
 Velocity is a vector quantity, which means that you must
use “+” or “–” to indicate direction
 It is based on displacement, not distance.
 i.e. Average speed must be positive, but average velocity
can be positive or negative

17. Speed vs. Velocity
 After a match, two tennis players rush to the net to shake
hands. If they both run towards each other at 3 m/s…
a) Same speeds / same velocities
b) Same speeds / different velocities
c) Different speeds / same velocities
d) Different speeds / different velocities

18. Position-Time
Graphs
Section 2.3

19. Position-Time Graphs
 …allow you to visualize 2-dimensional motion
 X-axis = time (usually in seconds)
 Y-axis = position (usually in meters)
 Straight lines represent an object traveling at constant
speed/velocity

20. Position-Time Graph Example
Time (s) Position (m)
0 0
2 10
4 20
6 30
8 40

21. Position-Time Graph Example
Time (s) Position (m)
0 0
2 10
4 20
6 30
8 40
 Calculate the slope of this line.

22. Position-Time Graphs
 Slope of a position-time graph gives velocity
 Units for slope/velocity are “m/s”.

23. Position-Time Graph Example
Time (s) Position (m)
0 0
0.5 2
1.0 4
1.5 4
2.0 4
2.5 3
3.0 2
3.5 5
4.0 8

24. 0
1
2
3
4
5
6
7
8
9
10
0 0.5 1 1.5 2 2.5 3 3.5 4
Position(m)
Time (s)

25. Position-Time Graphs
 Slope of a position-time graph gives velocity
 Units for slope/velocity are “m/s”.
 Think about it:
 What does a positive slope represent?
 What does a negative slope represent?
 What does a “0” slope look like?
 What does a “0” slope represent?

26. Equation of Motion
Section 2.4

27. Equation of Motion
 Works only with motion in a straight line and at a
constant velocity
 Units MUST be consistent!
𝒙 𝒇 = 𝒙𝒊 + 𝒗𝒕
 xf: final position
 xi: initial position
 v: velocity
 t: time

28. Important Note
 In the equation, “x” represents “position” even though “time”
is on the x-axis on the position-time graph
 This can be confusing. Be careful!

29. Example #1

30. Example #1

31. Example #1

32. Example #2
 The position-time equation of motion for a bunny hopping
across a yard is
𝑥 𝑓 = 8.3 m + 2.2
m
s
𝑡
a) What is the initial position of the bunny?
b) What is the bunny’s velocity?
c) Where will the bunny be after 8.0 seconds of hopping?

33. Example #3
 A bowling ball rolls with constant velocity from an initial
position of 1.6 m to a final position of 7.8 m in 3.1 s.
a) What is the position-time equation for the bowling ball?
b) At what time will the ball be in position 8.6m?

35. Test 1-2 Review

36. Topics Covered
 Comparing/calculating distance and displacement
 Calculating average speed
 Creating and analyzing position-time graphs
 Working with the equation 𝒙 𝒇 = 𝒙𝒊 + 𝒗𝒕