1. Unit 2
Motion in One and
Two Dimensions
Chapters 2 & 3 1

2. Motion
People walk, ride bikes, drive cars, etc. All the time we are dealing with motion…
What must you know in order to describe an object’s motion?
Just HOW FAST R U??? 3

3. Motion To describe motion we speak of:
Position - Where an object is; (as measured from some reference point)
Speed – an objects rate of change of position
Acceleration – an object’s rate of change of velocity 3

4. Motion is Relative
To describe motion we must do so from some understood point of view. This is called a FRAME OF REFERENCE (f.o.r.).
The Earth is the default f.o.r.
Describing the same motion from one f.o.r. may not be the same as another!?!
Can you think of an example? 3

5. Speed Speed- the rate of change of the position of an object.
The speed at any given moment is called instantaneous speed
The average speed is the TOTAL Dist. Divided by the TOTAL TIME
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6. So what’s Velocity? Velocity- describes both speed and direction.
35 mph north or 1500 m/s up
Velocity changes when speed OR direction change.
Can velocity change when speed is constant?
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7. Speed and Velocity Problems
Ex1: Find the speed of a car that goes 10 miles in 6.6 minutes.
Ex2: Find the speed and velocity of an airplane that flies 805 miles north in 2.3 hours. 4

8. Acceleration Acceleration- Rate of Change in velocity
Ave. Acceleration = a
Final velocity = Vf
Initial velocity = Vi
Time = t
What are the units?
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9. Acceleration requires change in velocity
Can you accelerate w/o changing speed?
Remember maintaining same speed but changing direction changes velocity, thus you have acceleration!
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10. Sample Problem What are your “givens?”
A flower pot falls off second story window sill. The flowerpot starts from rest and hits the sidewalk 1.5 seconds later with a velocity of 14.7 m/s. Find it’s average acceleration.
What are your “givens?”
Time: 1.5 s
Initial velocity: 0 m/s
Final velocity: 14.7m/s

11. Your Turn
Ex: If you run at a rate of 8.40 km/hour, how far will you run in 53 seconds?
Ex: What is the acceleration of a car that goes from m/s to 50.0 m/s in 1.00 minute?
Ex: What is the acceleration of a car that goes from 0 mph to 60.0 mph in 6.1 seconds? Is this a ‘fast’ car?

12. Weightlessness and Freefall
What is weightlessness?
An object is weightless when it accelerates downward at the accel. Of gravity…that is, when it is in freefall (no force other than
gravity is acting on the object)
Are you weightless in space??
The Physics Classroom.
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13. Free Falling Objects (How fast?)
All objects accelerate at the same rate under the influence of gravity.
But gravity does NOT pull with the same force on all objects!?!
Each second, a falling body will accelerate by about 10 m/s2 on Earth.
How fast will a dropped stone be going after 4 sec? (see table 2.2 on p. 17)
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14. Free Falling Objects (How far?)
Considering how fast an object falls is very different from considering how FAR it will fall, and is often a source of great confusion…
Each second, a body will fall a greater distance on Earth. Why?
About how far will a dropped bowling ball travel in the 1st second? In the 2nd second? (see Table 2.3 on p. 20)
Do IP2005 Activity 3.1
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15. Average velocity and final velocity of falling objects
A brick is dropped from a height of 30.0m.
What is the velocity of the brick after 2.0s?
d= 30.0m (total to ground)
t= 2.0s
v = ?
a = 9.8 m/s2 (due to gravity)
20 m/s
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16. Average velocity and final velocity of falling objects
A brick is dropped from a height of 30.0m.
If the brick takes 3.6s to hit the ground, what was its average velocity during the fall?
d = 30.0m
t = 3.6s
v = ?
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17. Is there another force acting on a falling object in Earth’s atmosphere?
Air resistance-
Force exerted by air on moving objects.
Acts in the opposite direction of the motion of the object.
depends on speed, mass, and surface area of the object.
Air resistance  as speed 
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18. Terminal Velocity
The largest velocity that can be reached by a moving object.
Falling objects accelerate at a decelerating rate (say that fast 10 times!) until they reach terminal velocity.
When terminal velocity is reached an object has no net force acting on it. Why??
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19. Terminal Velocity
When terminal velocity is reached an object has no net force acting on it. It keeps falling at a constant velocity.
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20. Just Hanging Out…
How long a body can remain in the air—HANG TIME—is important in diving, football, basketball, dancing, and other sports…
Objects launched at complementary angles will go the same distance but the ones launched at angles steeper than 45º will have more hang time…
Read p. 22 to learn the physics of hang time…
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21. What do you think?
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22. Graphing Motion
You can tell a lot about an object’s motion from looking at a graph of the motion…
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23. Distance vs. Time
To describe motion you must know the position of the object.
Speed can be determined from a distance vs. time graph.
The slope of the line is the speed.
What does a horizontal line show?
Distance vs. Time Graph
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24. Graphing Motion
What does the graph below tell us?
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25. Can you describe the motion???
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26. Describe the motion of cars A, B, and C
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27. Slope of velocity vs time graph
Tells the objects acceleration.
Acceleration can
be negative value.
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28. Speed (velocity) vs. Time graphs
Acceleration is equal to zero if velocity is constant.
Be sure to recognize speeding up and slowing down on a graph.
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30. Terminal Velocity
How would a graph of speed vs. time for a falling body under the influence of air resistance look?
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31. What’s your vector, Victor???
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32. Motivating Question: What is 4 + 7?
If you said “11”, you might be wrong! I say it can be 11…or -3…or any number in between 11 and -3!!!
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33. Vectors in the Real World: An Airplane flies east with an airspeed of 575 mph. If the wind is blowing north at 50 mph, what is the speed of the plane as measured from the ground?
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34. Vectors vs. Scalars
One of the numbers below does not fit in the group. Can you decide which one? Why?
35 ft
161 mph
-70° F
200 m 30° East of North
12,200 people
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35. Vectors vs. Scalars The answer is: 200 m 30° East of North
Why is it different?
All the others can be completely described with only a numerical magnitude. Numbers with that property are called SCALARS.
Numbers that need both magnitude and direction to be described are called VECTORS.
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36. Notation F Vectors are written as arrows.
The length of the arrow describes the magnitude of the vector.
The direction of the arrow indicates the direction of the vector…
On the board we will use the notation below… F
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37. Adding Collinear Vectors
When vectors are parallel, just add magnitudes and keep the direction.
Ex: 50 mph east + 40 mph east = 90 mph east
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38. Adding Collinear Vectors
When vectors are antiparallel, just subtract the smaller magnitude from the larger and use the direction of the larger.
Ex: 50 mph east + 40 mph west = 10 mph east
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39. Adding Perpendicular Vectors
An Airplane flies south with an air speed of 600 mph. If the wind is blowing west at 50 mph, what is the speed of the plane as measured from the ground?
Draw it…
What if the wind blew east?
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40. Adding Vectors Measure R with a ruler and measure θ with a protractor.
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41. Adding Vectors with scale diagrams
When vectors are not collinear, we must resort to drawing a scale diagram.
Choose a scale and a indicate a compass
Draw the vectors head-to-tail
Draw the resultant (answer)
Measure the resultant and the angle!
Ex: 600 mph S + 50 mph west = ??
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42. Adding Perpendicular Vectors
An Airplane flies south with an air speed of 600 mph. If the wind is blowing west at 50 mph, what is the speed of the plane as measured from the ground?
Draw it to scale…
You can use the Pythagorean theorem…
What if the wind blew east?
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43. Adding Nonperpendicular Vectors
An Airplane flies north with an air speed of 550 mph. If the wind is blowing 30º north of west at 50 mph, what is the speed of the plane as measured from the ground?
Draw it to scale…
You can use the Law of Sines and Cosines…
What if the wind blew north of east?
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44. Adding Vectors Measure R with a ruler and measure θ with a protractor.
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45. Vector Components Vectors can be described using their components.
The Components of a vector are two perpendicular vectors that would add together to yield the original vector.
Just think of the SHADOW of the vector on the x and y axes…
Components are often notated using
subscripts. F Fy Fx
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46. Special Triangles
In special triangles we can easily find lengths and angles…
3-4-5 right triangles
if the legs are 3 & 4, then the hypotenuse will be 5, and the angles will be 37.5º, 52.5º, and 90º
This works for all ratios of 3-4-5!
right triangles
If the legs are equal and the angles are 45º, then the hypotenuse is √2 (~1.414) times the leg!
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47. Vector Examples Find the sum of 45 km/hr north and 25 km/hr east.
Find the hypotenuse and angles of a triangle with legs of 20.0cm.
Find the components of the vector: 480 m/s at 40.0º N of E vector.
Draw it to scale, draw components to scale, measure… v vy
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48. Projectile Motion
Projectile Motion is defined as motion in two dimensions where the only external force acting on the system is gravity…
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49. Projectile Motion
What examples of projectile motion can you think of from your experience (think about sports…)
Do IP2005 activities , 5.4
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50. Think About It…
What happens when you are driving at a constant speed and throw a ball straight up in the air? How does it look to a passenger in the car? How does it look to an observer on the side of the road?
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51. Think About It…
Consider a gun that could “drop” a bullet from the end of the muzzle at the same instant that a bullet was fired from the end of the muzzle. Which would hit the ground first?
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52. Projectile Motion Fire/Drop a bullet demo
Throw a ball on a moving truck demo
Monkey shooting
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53. Projectile Motion
When an object is in projectile motion, the motion in the x and y directions are INDEPENDENT of each other!
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54. What do you think?
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55. Visualize It!
Draw a picture of an idealized soccer kick on Earth. Show seven “frames” of a high speed camera picture of the ball. Identify the vertical and horizontal velocity components in each of the seven frames. What can you say about the ball’s acceleration? What general statements can you make about it’s vertical and horizontal motion?
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56. Visualize It!
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57. Maximum Range of a Projectile
When an object is fired from the ground, we can determine—mathematically—the angle of launch that will yield the greatest range!
Why is this important?
What about when launched off a cliff?
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58. Satellite Motion
What happens when you fire a projectile with greater and greater speeds?
Satellites are just projectiles that keep falling but never hit the Earth! Why?
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59. The End 36