1. Motion

2. Motion
Motion is when an object’s distance is changing from another object.
Displacement: the amount of change in motion
Reference point: places or objects used for comparison to see if an object is in motion
We measure the way objects move in meters and seconds (over distance and time)

3. Displacement
displacement xi xf
Consider a train moving along a track – this is an example of one-dimensional motion
The train starts at an initial position, xi, and ends at a final position, xf. The change in position is called the displacement

4. Displacement Displacement = final position – initial position yf
∆y = yf - yi xi xf
∆x = xf - xi yi
∆ = delta = “change”
Displacement = final position – initial position
*Important formulas

5. Displacement Displacement can either be positive or negative
Negative displacement
Positive displacement
10m
30m
50m
70m
xf-xi = 10m-40m = -30m
xf-xi = 70m-40m = 30m
Displacement can either be positive or negative

6. Displacement Displacement does NOT always equal distance traveled x1
x3 = xf
10m
30m
50m
70m
Displacement = 50m-10m = 40m
Distance = 20m+40m+20m = 80m
Displacement does NOT always equal distance traveled

7. Displacement – Check for Understanding
A person runs 4 laps around a track. What’s their displacement? Distance?
Start/stop
Displacement = Distance = 1600 meters

8. Displacement – Check for Understanding
22 km
32 km
35 km
What is the total displacement and distance if you…
Go from home to school
Ditch school and go to the beach, then run home to tell your parents how much you learned at school today
Forget school, just go straight from home to the beach, and then back home

9. Speed Speed is the rate of distance covered over a period of time
Measured in meters per second
Describe the speed of the balls Do the balls ever have the same speed?
Comparing speed: Motion of balls is from left to right.
Ball A moves at constant speed.
Ball B starts off faster than A and slows down. There are two passing points.

10. Velocity
Average velocity is the speed and direction of an object over a time interval
average velocity = change in position = displacement
change in time time interval
Instantaneous velocity is the speed and direction of an object at a single moment in time (instant) – no formula

11. Example
During a race on level ground, Andrea runs with an average velocity of m/s to the east. What is Andrea’s displacement after 137 s? D
v = 6.02 m/s
t = 137s U
∆x = ? F
= (6.02 m/s)(137s) = 825m to the east A S

12. Velocity vs. Speed
Velocity tells you the direction and how fast you’re going, whereas speed only tells you how fast you’re going
v = displacement s = distance
time time

13. Velocity – Check for Understanding
Does the speedometer on a car read the car’s average velocity or instantaneous velocity?
If the speedometer of your car reads a constant speed of 40km/hr, can you say 100% for sure that the car has a constant velocity?
You drive around a race track at 28 mph and end up at the starting point. What was your average velocity for the trip?

14. Graphing Velocity
Velocity is shown as an object’s position at specific times along its path
Slope of a Line
Average Velocity

15. Graphing Velocity
Object 1 has positive velocity Object 2 has 0 velocity Object 3 has negative velocity
Instantaneous velocity is shown as a tangent line

16. Real Life Example D U F A v = ? t = 19.32s ∆x = 200 m
Jamaica’s Usain Bolt, hailed as the fastest man in the world, dominated the 200 m race in the Olympics with a time of s. What was his average velocity? Express your answer in miles per hour. D
v = ?
t = 19.32s U
∆x = 200 m F
= (200m)(19.32s) = m/s A

17. Real Life Example
Jamaica’s Usain Bolt, hailed as the fastest man in the world, dominated the 200 m sprint in the Olympics with a time of s. What was his average velocity? Express your answer in miles per hour.
10.35 m
1 s
1 km mi s min
1000 m km 1 min 1 hr
= mi
1600 hr A
= mph towards the finish line S

18. Acceleration
Acceleration is not just a change in velocity, it’s how fast that change happens.

19. Acceleration = ∆v/ t Def.: Change in velocity ∆v = vf – vi
Can be change in speed or direction
(speed up, slow down, or change direction)
Acceleration = ∆v/ t
∆v = vf – vi

20. Which cars are accelerating?B C
Cars B and C!

21. Which car has the greatest acceleration?B C
Car C!

22. Check for Understanding
Is this ball accelerating?
Yes! Because the direction is changing.

23. Acceleration
To measure it, you must know the initial velocity, the final velocity, and the time it takes to make the change.

24. Acceleration = change in velocity time
The unit for acceleration is m/s2.  v a = t

25. Acceleration
v is the difference between the final velocity (vf) and the initial velocity (vi).
v = vf - vi

26. Example 1
A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster?

27. Answer vf = 26 m/s vi = 10 m/s t = 2 s Acceleration = ∆v/ t
a = 26m/s – 10m/s
2 s
a = 16m/s 2s
a = 8m/s/s or 8m/s2

28. Examples 2-4 – Try them!
2. A car travels at 60 miles per hour around a curve. Is the car accelerating?
3. A car travels in a straight line at 60 mi/hr. Is the car accelerating?
4. A car goes from 0 mph to 60 mph in 6 seconds. What’s the car’s acceleration?

29. Answers:
1. Yes! Because it’s changing direction. 2. No! It’s not changing speed or direction. 3. -vf = 60 mph vi = 0 mph t = 6 s -a = vf – vi t -a = 60 – 0 mph = 10 m/s2 6 s

30. Graphing Velocity vs. Time
Constant acc.
No acc.
Increasing acc.

31. Graphing Speed
Constant speed
No motion
Increasing Speed

32. Examples
In your notes, describe the motion of the following race. Discuss the movement of each leg of the relay and include the terms, velocity, speed, acceleration, deceleration, rest.

33. Independent Practice In your seat, quietly work on the worksheets
Turn it into the inbox when you are finished.
If you do not finish, it is your homework.

34. Close
If Isaiha is skateboarding at a constant speed of 6 m/s and Jonathon is travelled 350 meters in a minute. Who is faster?
If Isaiha accelerates over 5 seconds for 10 meters and Jonathon accelerates 6 seconds for 10 meters, who is faster?