1. Kinematics – Part A
Physics 30S

2. Outcomes
S3P-3-02: Differentiate among position, displacement, and distance.
S3P-3-03: Differentiate between the terms “an instant” and “an interval” of time.
S3P-3-04: Analyze the relationships among position, velocity, acceleration, and time for an object that is accelerating at a constant rate. Include: transformations of position-time, velocity-time, and acceleration-time graphs using slopes and areas
S3P-3-05: Compare and contrast average and instantaneous velocity for non-uniform motion. Include: slopes of chords and tangents
S3P-3-06: Illustrate, using velocity-time graphs of uniformly accelerated motion, that average velocity can be represented as and that displacement can be calculated as
S3P-3-07: Solve problems, using combined forms of:

3. Instant vs. Interval of Time
What is an instant in time?
In physics, one point in time
For example, 3:
One glance at the clock
Idealized concept
An interval is a time period
For example, between 10:00 am and 11:00 am
3: to 3:

4. Measuring Time Intervals
Pencil, paper, stopwatch, hard surface
Ideas: helicopters, bottle pressure, trebuchet?
Distance (cm)
Time
Average Velocity 10 20 30 40 50 60

5. Measuring Time Instants
Pencil, paper, stopwatch, hard surface, ruler (overhead grid)
Ideas: camera, rubber ball
Time
Position
0:00.00

6. What Does it Mean on a Graph?
Interval: section
Instant: single point
More to come later...

7. Homework
Journal entry: Compare and contrast an instant and an interval. Use your ideas to guess what the difference is between instantaneous velocity and average velocity and between instantaneous acceleration and average acceleration.

8. Introduction to Kinematics

9. The Meaning of Negatives in Kinematics
Negatives indicate direction in kinematics!
Standard reference system
E/right is positive
W/left is negative
N/up is positive
S/down is negative
Think of a number line!

10. SI Units Système International des Unités (SI units)
Designed for consistency between all scientists
Always use SI units unless specifically instructed otherwise!!!
Quantity
Unit
Displacement m
Velocity
m/s
Acceleration
m/s2
Time s
Mass kg
Force N

11. Position, Displacement and Distance
Reminder:
Position: where are you right now
Distance: scalar, how far away are you from the reference point
Displacement: vector, distance and a direction

12. Averages Averages intend to paint the “overall” picture
In physics, we will discuss average velocity and average acceleration

13. Displacement, Velocity, and Acceleration - How Are They Related?
Remember, average velocity and acceleration are taken over an interval!
Δ is the Greek letter delta. It means “change in”, as in Δt is change in time.

14. Problem solving
Example 1 What is the average acceleration of a car which speeds up to 120 km/h from km/h in 1.5 seconds? Provide your answer in m/s2. aav = 3.7 m/s2 Example 2 What is the average velocity of a car which travels 25 m in 2.4 seconds? What is its velocity in km/h? Vav= 10. m/s

15. Working with Displacement, Velocity & Acceleration – Problem Solving
Example 3 How far does a car travelling 100. km/h travel in 3.5 s? Provide your answer in m. d = 97 m Example 4 What is the new velocity of the car from question 3 if it accelerates at 2.2 m/s2 for 3.0 s? Vf = 34 m/s

16. Homework
Physics, Concepts and Conceptions
Pg 30 #17, 19

17. Displacement, Velocity and Acceleration vs. Time Graphs

18. Position, Velocity, Acceleration
Which object is moving faster? A B

19. Displacement Time Graphs
We can graph the displacement travelled as a function of time
Use this graph to tell us about displacement, velocity and acceleration

20. Constant Acceleration
Many objects accelerate at a constant rate
Free fall (assume no air resistance)
Cart being pulled by an elastic
Useful to understand what constant acceleration means in terms of velocity
Velocity is increasing by the same amount each time interval
5 km/h, 10 km/h, 15 km/h, 20 km/h, etc.

21. Constant Acceleration

22. Slope Slope is rise over run, the change in y over x
In a displacement time graph, y is displacement and x is time
Remember velocity = displacement/time
In a displacement time graph, the slope is velocity
In a velocity time graph, the slope is acceleration

23. Constant Acceleration
Slope
Constant Acceleration
Slope

24. Area
The area under a graph is A = lw A = xy For a velocity time graph, y is velocity, x is time A = vt But d = vt, so The area under a velocity time graph is the displacement!

25. In general...
The formula for the area under a graph will change depending on the shape of the graph
We will always work with either constant velocity (square vt graph) or constant acceleration (triangle vt graph).

26. Constant Acceleration
Slope
Area
Constant Acceleration
Slope
Area

27. Graph Questions – Example 1
Imagine the d t graph provides the displacement for a rollercoaster. To two sig figs, what is the velocity of the rollercoaster?
V = 1.5 m/s

28. Graph Questions – Example 2
Imagine the v t graph provides the velocity for a new rollercoaster dropping down the track. To three sig figs, what is the acceleration of the rollercoaster?
a = 1.05 m/s2
Time (s)
Velocity (m/s)
1.00
1.05
2.00
2.10
3.00
3.15
4.00
4.20
5.00
5.25
6.00
6.30
7.00
7.35
8.00
8.40

29. Graph Questions – Example 3
Imagine the v t graph provides the velocity for a rollercoaster dropping down the track. What is the displacement of the rollercoaster at 3.00s?
d = 4.73m
Time (s)
Velocity (m/s)
1.00
1.05
2.00
2.10
3.00
3.15
4.00
4.20
5.00
5.25
6.00
6.30
7.00
7.35
8.00
8.40

30. Graph Questions – Example 4
Imagine the a t graph provides the acceleration for a rollercoaster dropping down the track. What is the velocity of the rollercoaster at 6.00s?
v = 13.2m/s

31. Graph Questions – Example 5
Time (s)
Displacement (m)
0.00
1.00
1.50
2.00
3.00
4.50
4.00
2.25
5.00
6.00
-2.25
7.00
-4.50
8.00
-6.75
9.00
10.00
11.00
-3.38
12.00
Imagine the d t graph provides the displacement for the rollercoaster’s track.
a)Explain what the rollercoaster is doing through each interval.
b) What is the velocity during each interval?

32. Graph Questions – Example 5 Solution
a)The rollercoaster travels at 1.50 m/s for 3.0 s, changes direction and heads back towards the start, travelling at m/s until 8.0s. The rollercoaster then stops until 9.0s, and then returns to the start at 3.38 m/s.
b) V1 = 1.50 m/s, V2 = m/s, V3 = 0.00 m/s, V4 = 3.38 m/s

33. Homework Physics, Concepts and Conceptions P.32 #28, 29, 30, 31

34. What about Instantaneous?
Imagine taking a smaller and smaller interval:
1 s, 0.1 s, 0.01s, 0.001s, s, etc
Repeating this infinitely, there would be no interval at all – you would have an instant
The intersection points would merge together to create...
A point of tangency!!!
Instantaneous velocity.ggb file

35. Tangent to the Curve
The slope of the tangent line to the displacement graph at a given point in time is the instantaneous velocity at that given point in time
Same relationship exists between velocity and instantaneous acceleration

36. Example 1
Find the instantaneous acceleration at 2.00s.

37. Example 1
Find the instantaneous acceleration at 4.00s. Pt 1(2.00,0.00) Pt 2(6.50, 36.00) a = 8.00 m/s2

38. Preview to Calculus
How do you tell when you’ve got the correct tangent line?
Tangent lines are difficult to draw – do your best
Tangent lines are like an estimation
To find the true instantaneous velocity or acceleration, we need calculus!

39. Homework
Physics, Concepts and Conceptions
P.34 # 36, 37, 38, 39, 43

40. Bringing Formulas into it
S3P-3-06: Illustrate, using velocity-time graphs of uniformly accelerated motion, that average velocity can be represented as and that displacement can be calculated as
Think back to the graph! The first formula is just slope!
The second is just the first formula where we are solving for d!

41. Problem Solving Here are the formulas we have available:
Pick one based on what you want to know and what is already known!
(We are assuming constant acceleration for #2)
S3P-3-07: Solve problems, using combined forms of:

42. Example 1
A puppy starts off at rest and accelerates at a constant rate to 8.0 m/s. Find his average velocity.
4.0 m/s

43. Example 2
A puppy starts off at rest and accelerates at a constant rate. If his displacement is 250 m north after 40 s, find his average velocity.
6.25 m/s

44. Example 3
A BMW stopped at a red light accelerates up to km in s. What is its average acceleration?
6.36 m/s2

45. Homework
Basic Kinematics worksheet

46. Lab

47. The Plan
Max Classes: 5
Time Intervals and Instants; Intro to kinematics (displacement, velocity, acceleration)
dt, vt, at graphs
Instantaneous acceleration
Formulas and Problem solving
Quiz