1. UNIT 3
MOTION

2. What do you think?
If you walk from home to school, and then immediately return to your home. If the distance from your home to school is 15 m, what is your ….
Distance?
Displacement?

3. What are some of the units we can measure displacement with?
What are some of the tools we use to measure displacement?

4. Distance or Displacement
Distance – the amount of space between two objects or points
Displacement – the overall change in position of an object.

5. Calculating Displacement
To calculate the displacement of an object you must know the beginning and ending point.
d = x - xo
d = displacement
X = final position
Xo = initial position

6. Sample Problem 1
Brendan walked from Walmart to his home, and there existed 300 m between the two. What is the…
Distance?
Displacement?

7. Sample Problem 2
Miranda walked from School to Subway and back at noon. If 20m existed between the school and Subway, what is the ….
Distance?
Displacement?

8. Speed or Velocity?
Speed – is a measurement that describes how far an object has moved in a certain period of time without indicating direction.
Velocity – is a measurement that describes how far an object has moved in a certain period of time, while at the same time indicating direction

9. Velocity calculations use displacement Speed calculations use distance
Both velocity and speed calculations use time.
Time – the duration between two events and is usually measured in seconds, minutes, or hours

10. Relating Velocity to Displacement and Time
Average Velocity (vave) - is the overall displacement divided by the total time it took to travel
The equation for average velocity is:

11. Instantaneous velocity – the velocity at which an object is traveling at a particular instant.
It is not affected by its previous velocity, or by how long the object has been moving.
The speedometer and radar gun were designed to measure instantaneous velocity.

12. Constant Velocity (uniform motion) – occurs when the velocity of an object remains the same over an extended period of time
E.g. Using Cruise Control on your car

13. Sample Problem 1
Claire bikes to school, a total displacement of m (SW). She has to slow down twice to cross busy streets, but overall the journey takes her 1080 seconds. What is Claire’s average velocity during the trip?

15. ANSWER 1 x = 450.0 m Xo = 0 m t = 1080 s V= ? v = 450 m/1080 s

16. Sample Problem 2
Taylor is trying to predict the time required to ride her bike to the nearby beach. She knows the distance is 5000 m and, from other trips, that she can average about m/s (E) including slowing down for climbing hills. Predict how long the trip will take.

17. Answer 2
∆t = s

18. Sample Problem 3
Jacob has a summer job helping with bison research. He notes that they graze (move and eat grass) at an average velocity of about 0.03 m/s (NW) for about s/d. What is the displacement, in meters, will the herd travel in two weeks (14 d)?

19. Answer 3
∆d =

20. Homework
Neil is riding a cow at a velocity of m/s for a period of s. What is Neil’s displacement?
Melissa is driving for s if she drove 5000 m what was her velocity?

21. Homework
Questions 1 – 6 on page 358

23. Changing Units
All final calculations in Physics should be in meters and seconds
Unit
Equivalence to 1 m Km
1000 m hm
100 m d
10 m m
1 m dm
0.1 m cm
0.01 m mm
0.001 m
Unit
Equivalence to 1 s
1 day s
1 h
3 600 s
1 min
60 s

24. Convert the following to the appropriate units:
1) 2 hours
2) 100 km
3) 7 cm
4) 5 min
5) 2 km/s
6) 10 m/h
7) 500 km/h

25. What do you do when you have two different velocities?
In some problems you will be given more than one velocity (an initial velocity and a final velocity)
In most cases your initial velocity is 0 and is not stated in the problem
In other cases the initial velocity is given a concrete value due to the fact that the object is in motion at the beginning of the problem and the velocity is altered at some point (either faster or slower).

26. Two Velocities
In situations where there are two velocities (and only displacement and time) in most cases we will use the following formula to determine the average velocity of the object

27. Sample Problem 1
Courtney is sitting at a red light in her red corvette. The light turns green and Kristen instantaneously guns the engine of her car. If 10 seconds later Courtney is traveling at a velocity of 90 km/h in a northern direction (in a 50 km/h speed zone) what is her displacement?

28. Answer
= (25 m/s + 0 m/s)/2
= 12.5 m/s
d = (12.5 m/s)(10s)
d = 125 m

29. Sample Problem 2
Lucas and Brandon are at Walmart looking for a video game. They are walking down the video game isle at a velocity of 0.5 m/s. They happen to spot Miss Cook at the store and they want to avoid her seeing them in the isle with the video games, so they quickly leave the isle traveling at a velocity of 0.9 m/s. If it only took Lucas and Brandon 3 seconds to exit the isle, what was their displacement?

30. X = 2.1 m

31. Sample Problem 3
Patrick and Jeremy are driving in Sussex at 60 km/h towards Apohauqui. Once they reach the highway they speed up to a velocity of 110 km/h within 30 seconds. What was their displacement within this time period.

32. x = m

33. Sample Problem 4
Chrissy is walking towards the mall at a velocity of 0.4 m/s. She sees a 50% off sale sign in the window and starts running towards the store. If her final velocity is 2.3 m/s (she is wearing stilettos). If the displacement between the store and where she spotted the sign is 0.3 km, how long did it take her to reach the store.

34. t = s

35. Sample Problem 5
Blair and Nathan are snowboarding at Poley Mountain. If at the top of the hill they are traveling at a velocity of 3 m/s and it takes them a total time of 2 minutes to reach the bottom of the hill, a displacement of 500 m. How fast were Blair and Nathan traveling at the bottom of the hill?

36. = 4.2 m/s
V = 5.4 m/s

37. Sample Problem 6
Sam is snowshoeing around the trail behind the school for gym class. Sam has never used snowshoes before but quickly picks up the technique. If Sam traveled with an final velocity of 3.0 m/s and it took her 10 minutes to travel the 1 km long route. What was Sam’s initial velocity?

38. = 0.4 m/s

39. Homework
Ben leaves his home and drives towards the train station with a final velocity of 30 m/s. If it took Ben 10 minutes to reach the train station how far did he travel.
Holly is riding her bike to the local KFC. It takes Sally 10 min to reach KFC which is 4.7 km away. What is Holly’s initial velocity if she ends the trip with a velocity of 17 m/s.

40. Review of Variables in Graphing
Independent Variable – the variable that changes over the course of an experiment in order to compare results.
Dependent Variable – the variable that changes as a result to changes in your independent variable

41. Dependent Variable
Y - axis
X - axis
Independent Variable

42. Graphing Expectations
The title of your graph must be placed at the top of your graph
Label your x and y axis with the appropriate terms and units
Label the end of your axis with either an x or y
Pick an appropriate scale for your values

43. Displacement Time Graphs
When observing or constructing a displacement time graph your time is always your independent variable (x-axis), while your displacement is your dependent variable (y-axis)
The slope represents the velocity (the relationship between the dependent and independent variable)
The greater the velocity the larger the slope

44. How to Interpret Displacement Time Graphsy
In this graph the object is not in motion.
How can you tell this from the graph?
Displacement (m) x
Time (s)

45. How to Interpret Displacement Time Graphsy
In this graph the object is moving with a constant velocity.
How can you tell this from the graph?
Displacement (m) x
Time (s)

46. In this graph the velocity is not constant.
How can you tell this from the graph?
How would you calculate average velocity for this graph? y
Displacement (m) x
Time (s)

47. How to Interpret Displacement Time Graphsy
In this graph there is no velocity.
How can you tell this from the graph?
Displacement (m) x
Time (s)

48. How to Interpret Displacement Time Graphs
In this graph you would solely use the values of xi and xf to determine the displacement of the object, in order to calculate velocity. Why? y
Displacement (m) x
Time (s)

49. How to construct a displacement time graph
Plot your points using an appropriate scale along your x and y axis
Chose two points from your line of best fit and use them to calculate the slope of the line (velocity)

50. Graphing displacement and time
d (m)
t (s) 1 2 4 5 8 9 11 15

52. Defining Acceleration
Acceleration (a) – is the rate of change in velocity in a specific time interval.
Constant Acceleration – changing an objects velocity at the same rate each second.
Average Acceleration – is the average rate of change in velocity of an object.

53. Sample Problem 1
Neil accelerates from rest at a rate of 2.5 m/s2 for 1.5 s. What was Neil’s final velocity?

54. ANSWER 1
v = 0 m/s + (2.5 m/s2)(1.5s)
v = 3.8 m/s

55. Sample Problem 2
Ty is skateboarding down a hill and changes his velocity from 0.5 m/s to 1.9m/s. If his average rate of acceleration down the hill is 0.40m/s2, for how long did it take Ty to reach his final velocity?

56. ANSWER 2
t = 3.5 s

57. Homework
Taylor is driving through Tim Horton’s drive thru with an acceleration rate of 6 m/s2 for 60 s. What was her velocity?
Matt and Jesse are best friends who are skiing at Poley. They start at the top of the hill with a velocity of 0 m/s and at the bottom they have a velocity of 10 m/s. If it takes them 50 s to get to the bottom of the hill what is their rate of acceleration?
Chrissy is horse back riding down Main Street. Chrissy wants to make the green light so she accelerates her horse at a rate of 0.5 m/s2 to a velocity of 6 m/s. How long did this take Chrissy?

58. Kimbo Slice is riding a tricycle from one end of the octagon to the other. If it takes Kimbo Slice 500 s to cover the 12 m. What was Kimbo Slice’s acceleration rate?

59. Sample Problem 3
Kelsie is moving at 1.8m/s near the top of a hill. 4.2 s later she is at the bottom of the hill and traveling at 8.3 m/s. What is her average acceleration?

60. ANSWER 3
Vo = 1.8 m/s
∆t = 4.2s
V = 8.3 m/s
a = ?
a = 1.5 m/s2

61. Acceleration While Slowing Down
Acceleration while slowing down is calculated in the same manner as acceleration while speeding up. The only difference is that the acceleration is represented with a negative sign.

62. Sample Problem 5
In a race, a car traveling at 100km/h comes to a stop in 5.0 s. What is the average rate of acceleration?
Vo = 100 km/h
V = 0
t = 5.0 s
a = ?

63. Homework
Lucas is walking down the street, while drinking pop, with a velocity of 3 m/s. He sees a huge crack in the sidewalk and trips (spilling his pop). If the time between when he saw the crack and when he falls is 10 s. What was his rate of acceleration?