1. 1D Motion
Physics

2. Vector and Scalar Quantities
Vector quantities need both magnitude (size) and direction to completely describe them
Ex: Displacement, Velocity, Acceleration
Scalar quantities are completely described by magnitude only
Ex: Distance travelled, speed, Energy, time

3. Position

4. Frame of Reference Practice
Describe your position in three different reference frames.

5. Displacement

6. Displacement Isn’t Distance
The displacement of an object is not the same as the distance it travels
Ex: Throw a ball straight up and then catch it at the same point you released it
The distance is twice the height – 2h
The displacement is zero h

7. Position, Displacement and Distance travelled – Practice WB
State the position of the car at:
A: ____
E: ____
State the distance travelled from:
A to B: _____
A to D: _____
A to F: ______
State the displacement of the car from:
A to F: _____

8. Write:
What is the difference between position, distance travelled and displacement.

9. Average Speed
The average speed of an object is defined as the total distance traveled divided by the total time elapsed
Scalar quantity
Ignores any variations in the object’s actual motion during the trip
The total distance and the total time are all that is important
SI units = m/s

10. Average Velocity
The average velocity is rate at which the displacement occurs
Direction will be the same as the direction of the displacement (time interval is always positive)
+ or - is sufficient for now
SI Units of velocity are m/s
(may need to be converted)
Ignores actual movement as well

11. Average Speed and Velocity - Practice - wb
State the Average Speed if it takes 20 seconds to travel :
From A to B: ______
From A to D: ______
From A to F: _______
From F to A: _______
State the Average Velocity if it takes 20 seconds to travel:
From A to B: _______
From A to D: _______
From A to F: ________
From F to A:

12. Speed vs. Velocity
Cars on both paths have the same average velocity since they had the same displacement in the same time interval
The car on the blue path will have a greater average speed since the distance it traveled is larger

13. Practice #1 - WB
An athlete swims from the north end to the south end of a 50.0 m pool in 20.0 seconds and makes the return trip to the starting position in 22.0 s.
What is the average velocity for the first half of the swim? ________
What is the average velocity of the second half of the swim? _______
What is the average velocity for the round trip? _______

14. Practice #2
Example: Two friends bicycle 3.0 kilometers north and then turn to bike 4.0 kilometers east in 25 minutes.
a) What is their average speed?
b) What is their average velocity?

15. Uniform Motion/Constant Velocity
Uniform motion = constant velocity : a =0
The displacement changes by equal amounts in equal intervals of time
Time (s) 1 2 3 4
Distance (m)
Velocity (m/s)
Acceleration (m/s2)

16. HP: Uniform Motion Formula
Displacement at t = 0 is xo
Displacement at time t is x
And,
Then: x = xo+vt
t = 0
t = t xo x

17. HP: Uniform Motion Examples1.
a. A car initially at position -5.0 m has a uniform velocity of 7.0 m/s.
At what position is it 4.0 seconds later?
b. A car initially at position 4 m has a velocity of -3 m/s.
At what time does it reach a position of -20 meters?
What distance does the car travel in this time?

18. Physics 500 Lab
Regular Physics only

19. HP - Instantaneous Velocity
The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero
The instantaneous velocity indicates what the velocity is at every point of time, not just over a period of time
Example: Car is speeding up and slowing down – average velocity doesn’t tell us much about its movement.

20. Position vs. Time Graphs
Computer/Vernier in groups

21. Graphical Interpretation: distance vs. time - wb
s/m
Not Moving
Constant velocity
Constant velocity of 5ms-1
Negative velocity of 5ms-1
Starting from rest and accelerating
Starting 20 meters away at a fast pace and slowing down.
t/s

22. Graphical Interpretation of Velocity
Velocity can be determined from a position-time graph
Average velocity equals the slope of the line joining the initial and final positions of a distance – time graph. UNITS can prove it!
An object moving with a constant velocity will have a graph that is a straight line

23. *Average Velocity, Constant
The straight line indicates constant velocity
The slope of the line is the value of the average velocity

24. Average Velocity, Non Constant
The motion is non-constant velocity
The average velocity is the slope of the blue line joining two points

25. HP - Instantaneous Velocity on a Graph
The slope of the line tangent to the position-vs.-time graph is defined to be the instantaneous velocity at that time
The instantaneous speed is defined as the magnitude of the instantaneous velocity

26. 100m Split times - discussion

27. Acceleration

28. Now Try Practice B

29. Velocity vs. Time graphs
Computer/Vernier in groups

30. Graphical Interpretation: velocity vs. time
v/ms-1
Not moving
Constant velocity
Accelerating
Slowing down
t/s

31. HP - Using Velocity vs. time graphs to calculate displacement.
The area below a velocity – time graph represents the total displacement between those two times.
Prove it with UNITS!
Example:

32. HP - Graphical Interpretation of Acceleration
Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph – UNITS can prove it!
HP - Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph

33. Average Acceleration

34. Uniformly Accelerated Motion
Uniformly Accelerated Motion = Constant Acceleration
The velocity changes equal amounts in equal amounts of time.
Time (s) 1 2 3
Distance (m) 10 23
Velocity (m/s) 5 15
Acceleration (m/s2)

35. For each simulation, state whether each is positive, negative or zero.
HP - Some practice
For each simulation, state whether each is positive, negative or zero.
Displacement
Velocity
Acceleration

36. HP - Some Practice

37. Quiz #1
Definitions and finding distance, displacement, speed, velocity, acceleration
Calculations of average velocity (Practice A) and average acceleration (Practice B)
Interpreting, creating and finding values from position vs. time and velocity vs. time graphs

38. Problem-Solving Requirements
Read the problem
Draw a diagram!!
Choose a coordinate system, label initial and final points, indicate a positive direction for velocities and accelerations
Label all known quantities, be sure all the units are consistent
Convert if necessary
Choose the appropriate kinematic equation(s) that has only one variable that you don’t have the value for.
Solve for the unknowns
You may have to solve two equations for two unknowns. Be careful of Negatives!
Check your results
Estimate and compare
Check units

39. Constant Acceleration Formula

40. 2. A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?

41. Constant Acceleration Example
3. An object starting with an initial velocity of 5.0 m/s undergoes constant acceleration. After 10 seconds its velocity is found to be 35 m/s.
What is the acceleration?
Is it possible to know its position?
4. An object starting with an initial velocity of m/s undergoes a constant acceleration of m/s2.
When does it reach a velocity of 14 m/s?
Now Try: Practice D

42. Another Constant Acceleration Formula

43. Example
5. A racing car reaches a speed of 42 m/s. It then begins a uniform negative
acceleration, using its parachute and braking system, and comes to rest
5.5 s later. Find the distance that the car travels during braking.
Now Try: Practice C

44. Another Constant Acceleration Formula

45. 6. A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s2. What is the velocity of the stroller after it has traveled 4.75 m?
Now Try Practice E

46. Relationship Between Acceleration and Velocity
Uniform velocity (shown by red arrows maintaining the same size)
Acceleration equals zero

47. Relationship Between Velocity and Acceleration
Velocity and acceleration are in the same direction
Acceleration is uniform (blue arrows maintain the same length)
Velocity is increasing (red arrows are getting longer)
Positive velocity and positive acceleration

48. Relationship Between Velocity and Acceleration
Acceleration and velocity are in opposite directions
Acceleration is uniform (blue arrows maintain the same length)
Velocity is decreasing (red arrows are getting shorter)
Velocity is positive and acceleration is negative

49. HP - Uniformly Accelerated Motion - Equations
Used in situations with uniform/constant acceleration and uniform/constant acceleration ONLY!!!!!

50. Deriving the equations

51. HP - Examples:
7. Nathan accelerates his skateboard uniformly along a straight path from rest to 12.5 m/s in 2.5 sec. A. What is Nathan’s displacement during this time interval? B. What is Nathan’s average velocity during this time interval?

52. HP - Example:
8. A body at the origin has an initial velocity of -6.0 ms-1 and moves with an acceleration of 2.0 ms-2 . When will its displacement become 16 m? 

53. HP - Example:
9. A car starts from rest and travels for 5 seconds with a uniform acceleration of +1.5m/s2. The driver then applies the brakes, causing a uniform acceleration of -2 m/s2. If the brakes are applied for 3 seconds, how fast is the car going at the end of the braking period, and how far has it gone from its start?

54. Frames of Reference Video
We are used to measuring velocities with respect to observers who are “at rest” however, if you are moving, you are in your own frame of reference and observe things accordingly.

55. Relative Motion and Frames of Reference
You are waiting for a bus
A bus passes you at 20 m/s
A passenger is walking on the bus at a speed of 1 m/s
What is his relative velocity if he walks in the direction the bus is going
What is his relative velocity if he walks in the direction opposite the bus.

56. Relative Motion and Frames of Reference Example
1. Car 1 – 35 km/hr Car 2 – 40 km/hr Car 2 overtakes Car 1 because it is going faster What is the relative speed of Car 1 to Car 2

57. Free Fall and Air resistance

58. Galileo Galilei
Galileo formulated the laws that govern the motion of objects in free fall
Also looked at:
Inclined planes
Relative motion
Thermometers
Pendulum

59. Free Fall Video Galileo’s thought experiment
All objects moving under the influence of gravity only are said to be in free fall
Free fall does not depend on the object’s original motion
All objects falling near the earth’s surface fall with a constant acceleration
The acceleration is called the acceleration due to gravity, and indicated by g

60. Acceleration due to Gravity
Symbolized by g
g = 9.8 m/s² or 9.81 m/s2
When estimating, use g » 10 m/s2
g is always directed downward
toward the center of the earth – typically negative in the equations
Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion

61. Free Fall – an object dropped
Initial velocity is zero
Let up be positive
Use the kinematic equations
Generally use y instead of x since vertical
Acceleration is g = m/s2
U = 0
a = g

62. Free Fall – an object thrown downward
a = g = m/s2
Initial velocity  0
With upward being positive, initial velocity will be negative

63. Free Fall -- object thrown upward
Initial velocity is positive
The instantaneous velocity at the maximum height is zero
a = g = m/s2 everywhere in the motion
v = 0

64. Thrown upward, cont. The motion may be symmetrical
Then tup = tdown
Then v = -u
The motion may not be symmetrical
Break the motion into various parts
Generally up and down

65. Non-symmetrical Free Fall
Need to divide the motion into segments
Possibilities include
Upward and downward portions
The symmetrical portion back to the release point and then the non-symmetrical portion

66. Free fall Example #1
A pebble is dropped down a well and hits the water 1.5 seconds later. Using the equations for motion with constant acceleration,
Determine the distance from the edge of the well to the water’s surface.
For the same well, determine how long it would take to hit the water if it was thrown down with a speed of 1 m/s.

67. Free Fall Example #2
A person throws a ball upward into the air with an initial velocity of 15.0 m/s. Calculate:
How high it goes
How long the ball is in the air before it comes back to his hand
How much later the ball hits the ground if he didn’t catch it, if his hand is 1 meters above the ground.

68. Free Fall Example #3
A mass is thrown upwards with an initial velocity of 30 m/s. A second mass is dropped from directly above, a height of 60 m from the first mass, 0.5 s later.
When do the masses meet?
How high is the point where they meet?

69. Falling Cats
Study was done to find out how cats survived long falls.
Results: The higher the cats were dropped from, the less injuries occurred.
WHY????

70. Investigating Air resistance
Take a few minutes to experiment with dropping some objects and thinking about your everyday experiences.

71. Forces and Acceleration
Think of the times when you are accelerating: in the car speeding up, in the car slowing down, on a roller coaster, skiing off a jump.
Now think of the times when you are not accelerating – travelling at a constant speed in the car, sitting at rest at your desk.
How do you feel? If your eyes are closed, can you feel whether you are accelerating or not?

72. Air Resistance and Terminal Velocity
V = 10m/s
T =2 V=20m/s
T =3
V=30m/s