1. One Dimensional Motion
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One Dimensional Motion
Physics I

2. 1 kg 1000 g 1 g 1000 mg 1 m 1000 mm 100 cm 1 cm 10 mm 1 min 60 sec
Metric Conversions YOU must know.
1 kg
1000 g
1 g
1000 mg
1 m
1000 mm
100 cm
1 cm
10 mm
1 min
60 sec
1 hour
3600 sec
1 L
1000 mL

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Speed and Velocity
MHS Physics

4. Magnitude
Size

5. Scalar – Quantity with magnitude only
Vector – Quantity with magnitude and direction
Scalars (Magnitude)
Vector (Magnitude and Direction)
Distance (20 m)
Displacement (20 m, North or +20 m)
Speed (20 m/s)
Velocity (20 m/s, North or +20 m/s)
Mass (20 kg)
Acceleration (+20 m/s2)
Time (20 seconds)

6. Distance vs. Displacement
Displacement or change in position
Final position, x
Initial position, xo
(x-xo=x)
Displacement can be negative!
Cutnell & Johnson

7. Distance vs. Displacement

10. Distance and Displacement
For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W.
Net displacement D is from the origin to the final position: D
8 m,E x
x = +8
D = 4 m, W
12 m,W
What is the distance traveled?
20 m !!
Author: Tippens, P. (2007)

11. Definition of Speed
Speed is the distance traveled per unit of time (a scalar quantity).
s = = d t
20 m
4 s A B
d = 20 m
Time t = 4 s
v = 5 m/s
Not direction dependent!
Author: Tippens, P. (2007)

12. Definition of Velocity
Velocity is the displacement per unit of time. (A vector quantity.)
North A B
d = 20 m
Time t = 4 s
x=12 m
v = 3 m/s East
East
Direction required!
Author: Tippens, P. (2007)

13. Constant Speed
Ticker Tape Diagrams:
Which diagram represents a faster constant speed?

14. Means change in, so subtract!
Average velocity Average Speed =
Means change in, so subtract!
What is the difference in the car’s average velocity in part a) and part b)?
t = s
Cutnell & Johnson

15. Example 1. A runner runs 200 m, east, then changes direction and runs 300 m, west. If the entire trip takes 60 s, what is the average speed and what is the average velocity?
Recall that average speed is a function only of total distance and total time:
s2 = 300 m
s1 = 200 m
start
Total distance: s = 200 m m = 500 m
Avg. speed 8.33 m/s
Author: Tippens, P. (2007)

16. Example 1 (Cont.) Now we find the average velocity, which is the net displacement divided by time. In this case, the direction matters.
xo = 0
t = 60 s
x1= +200 m
xf = -100 m
x0 = 0 m; xf = -100 m
Direction of final displacement is to the left as shown.
Average velocity:
Note: Average velocity is directed to the west.
Author: Tippens, P. (2007)

17. Example 2. A sky diver jumps and falls for 625 m in 14 s
Example 2. A sky diver jumps and falls for 625 m in 14 s. After chute opens, he falls another 356 m in 142 s. What is average speed for entire fall?
625 m
356 m
14 s
142 s A B
Total distance/ total time:
Average speed is a function only of total distance traveled and the total time required.
Author: Tippens, P. (2007)

18. From a Graphical View:
When finding the average velocity for each interval, what feature of the graph are you calculating? (Math term)
Cutnell & Johnson
Average velocity Average Speed =

19. Interpret the motion of the object in the graph below.
How fast (average velocity) is the object traveling in each interval of time? How can this be determined?
What is the average velocity of the entire trip?
What is the average speed of the entire trip?

20. - + - + Warm-up + 0-10 sec, 40-55 sec 15-40 sec
Notice the correlation between the signs of the slopes and the direction it is traveling in each time interval - + - +
During which time intervals did it travel in a positive direction?
During which time interval did it travel in a negative direction?
0-10 sec, sec
15-40 sec

21. Average Speed and Instantaneous Velocity
The average speed depends ONLY on the distance traveled and the time required.
The instantaneous velocity is the magnitude and direction of the speed at a particular instant.
(v at point C) A B
s = 20 m
Time t = 4 s C
Author: Tippens, P. (2007)

22. Velocity vs. time graph 5 s 1 2 3 4 -3 m/s2
Positive Velocity indicates positive displacement 5 s -3
What direction (pos. or neg.) is the object traveling during 0-1 sec?
When is the object traveling in a neg. direction?
What is the object doing during the 1-2 second interval?
What is the average speed from 2-3 seconds?
What is the instantaneous speed at 3.5 seconds?

23. Average Acceleration
The rate of change in instantaneous velocity, either magnitude, direction, or both.
Acceleration can be either be positive or negative – vector quantity

24. Graph Relations
What type of relationship exists between the position or displacement and time during constant acceleration

25. How is instantaneous velocity determined from a curve graph?
Graph Relations
How is instantaneous velocity determined from a curve graph?

26. What does the slope of velocity determined from a curved graph?
Graph Relations
What does the slope of velocity determined from a curved graph?

27. What is the instantaneous speed of the object at point B?
Practice
What is the instantaneous speed of the object at point B?
-2 m/s
+2 m/s
-1.3 m/s
+1.3 m/s

28. Interpret the graph below and draw a position vs
Interpret the graph below and draw a position vs. time graph and an accel. vs. time graph.
Practice T Δx 10 25 20 75 30
175 40
250 50
200 +a -a 50 75 25 50 50
-50
When is the object accelerating? How can this be determined?

29. Summary:
Corresponding Shapes of Motion Graphs with Constant Acceleration d v d v d v d v

30. GRAPH RELATIONSHIPS

31. Graph Relationships

32. Determine displacement from a velocity vs. time graph
How do I determine displacement from a velocity vs. time graph?
When is it negative?

33. G A H F B C E D Velocity vs. Time Graphs
1. When was he traveling in a positive direction? 2. When was he traveling in a negative direction? 3. When was he at rest? 4. During what time intervals did he travel at a constant velocity? 5. During what time interval did he travel the greatest distance?
6. When does he have a positive acceleration?
7. When is he increasing his speed? Decreasing his speed?
8. What is the average acceleration during interval A?
9. What is the instantaneous acceleration at 2.5 seconds?

34. Constant speed Acceleration Accleration
Acceleration is a vector quantity and can be positive or negative
How does the distance between dots change as an object acceleration?

35. Three Ways to Accelerate
Hewitt, P. Conceptual Physics.

36. Motion Equations
What does each of the variables represent in the motion equations?

37. A car starts from rest with an acceleration of 2m/s2
A car starts from rest with an acceleration of 2m/s2. What is its velocity after it has traveled 200m?

38. Sample Problems
Space to work
A car starts from rest and reaches a velocity of 40m/s in 10s. What is its acceleration?

39. A car travels 300m East, then 100m West, and finally 300mW in 1hour
A car travels 300m East, then 100m West, and finally 300mW in 1hour. What is the average speed? What is the average velocity?

40. YOUR TURN!
A ball starts with an initial speed of 2m/s. It accelerates at 0.5m/s2 in a time of 5 seconds. How far did it travel?

41. YOUR TURN!!!
How long will it take to bring the car to a stop from an initial velocity of 10m/s with a deceleration of 2m/s2

42. Example 3 (No change in direction): A constant force changes the speed of a car from 8 m/s to 20 m/s in 4 s. What is average acceleration? +
t = 4 s
v1 = +8 m/s
v2 = +20 m/s
Step 1. Draw a rough sketch.
Step 2. Choose a positive direction (right).
Step 3. Label given info with + and - signs.
Author: Tippens, P. (2007)

43. Example 3 (Continued): What is average acceleration of car?+
v1 = +8 m/s
t = 4 s
v2 = +20 m/s
Step 4. Recall definition of average acceleration. 2
Author: Tippens, P. (2007)

44. Example 4: A wagon moving east at 20 m/s encounters a very strong head-wind, causing it to change directions. After 5 s, it is traveling west at 5 m/s. What is the average acceleration? (Be careful of signs.) +
vf = -5 m/s
vo = +20 m/s
Step 1. Draw a rough sketch.
Step 2. Choose the eastward direction as positive.
Step 3. Label given info with + and - signs.
Author: Tippens, P. (2007)

45. Choose the eastward direction as positive.
Example 4 (Cont.): Wagon moving east at 20 m/s encounters a head-wind, causing it to change directions. Five seconds later, it is traveling west at 5 m/s. What is the average acceleration?
Choose the eastward direction as positive.
Initial velocity, vo = +20 m/s, east (+)
Final velocity, vf = -5 m/s, west (-)
The change in velocity, Dv = vf - v0
Dv = (-5 m/s) - (+20 m/s) = -25 m/s
Author: Tippens, P. (2007)

46. + Example 4: (Continued) East vf = -5 m/s aavg = = Dv Dt vf - vo
vo = +20 m/s
vf = -5 m/s
East
Dv = (-5 m/s) - (+20 m/s) = -25 m/s
aavg = = Dv Dt
vf - vo
tf - to
a =
-25 m/s
5 s
a = - 5 m/s2
Author: Tippens, P. (2007)

47. A student walks 3 meters, North and then 4 meters, South in 6 seconds
A student walks 3 meters, North and then 4 meters, South in 6 seconds. What is the average velocity?
1.167 m/s, North
1.167 m/s, South
0.167 m/s, North
0.167 m/s, South

48. The sign of the velocity of an object represents the
The magnitude
The direction
The acceleration
The speed

49. Corresponding Acceleration vs. Time Graph

50. Describe the motion of the object.
Initial position is 0.0 m.
5.0

51. Which graph best matches the statement?

54. Graph Shapes
Linear; y = mx +b
Quadratic: y = x2
Inverse: y = 1/x
Inverse Square : y = 1/x2

55. FREE FALL
Galileo discovered objects fall at the same rate when air resistance is very small.
Which strikes the ground first, a coin or a feather, in a vacuum?

56. GRAVITATIONAL ACCELERATION CONSTANT
Average gravitational acceleration on Earth is constant 9.8m/s2 and is always in a downward direction. The speed of an object thrown upward is equal to its speed on the way down at the same height.
What is the gravitational acceleration constant?

57. Acceleration is independent of mass!

58. When an object is thrown upward or dropped, does gravity ever change in magnitude or direction?
Displacement, velocity, and acceleration are all down and considered to be negative.
Acceleration – gravity is always acting on an object on Earth.

59. Graphical analysis of free fall
On a velocity vs. time graph, how can you tell when the object is turning around?

60. Graphical analysis for free fall
Does the slope of a velocity vs. time graph change direction (at all) when an object is in free fall?

61. A ball is thrown vertically upward with an initial velocity of 20 m/s
What is its displacement after 2seconds?

62. A ball is thrown vertically upward with an initial velocity of 20 m/s
What is it’s velocity after 2 seconds?

63. A ball is thrown vertically upward with an initial velocity of 20 m/s
What is its maximum height?

64. A ball is dropped 50cm from the ground
A ball is dropped 50cm from the ground. How long does it take to hit the ground?

65. A toy rocket is launched with a speed of 3 m/s
How long is it in the air? (TIME UP AND DOWN)

66. A toy rocket is launched with a speed of 3 m/s
Calculate the maximum height of the rocket.

67. Credits:
Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons.
Foxtrot Cartoon: Bill Amend. Received from 2007 AP Conference.
Hewitt, P. [Illustrations]. Conceptual Physics.
Nave, R. (2010). Hyperphysics.[Illustration]. Permission granted to use illustrations. Retrieved from
Tippens, P. (2007). Chapter 6A Acceleration [PowerPoint Slides]. Received from 2007 AP Conference.