1. Learning Target 3: Velocity
3.1 I can calculate speed and velocity
3.2 I can distinguish between speed and velocity
3.3 I can use a graph to determine and describe motion velocity, and other elements of the graph

2. Why?? Motion happens all around us
Cars, people, soccer balls, etc.
How do we begin to see and analyze motion as an engineer does?

3. What is motion?
Motion: change of the position of an object with respect to time
Ouch.

4. Distance Definition: Total length traveled
What distance did the turtle cover?

5. Displacement
Definition: change in the position of an object from its beginning point
Formula: Δx = xf-xi xf xi Δx

6. Distance vs. Displacement
Displacement = change in position from start
Distance = total length traveled
What total distance did the turtle cover?
What was his displacement?

7. Displacement Positive displacement: moving up or forward
Negative displacement: moving down or backward

8. Quick Checks What is the difference between distance and displacement?
What letter do we use to represent position?

9. Quick Checks +
4 m +
2 m
2 m -
4 m -

10. Speed Definition: rate of change in distance with respect to time
Formula: speed = distance/time

11. Average Velocity
Definition: rate of change in displacement with respect to time
Formula: vavg = xf – xi = displacement = d
tf – ti time t
Units: length/time

12. Average Velocity Can be positive or negative
Depends on sign of displacement
Positive velocity = moving forward
Negative velocity = moving backward

13. Velocity vs. Speed
Velocity is a VECTOR quantity, which means it describes motion with both magnitude and direction
Rate of change of DISPLACEMENT with respect to time
Speed is a SCALAR quantity, which means it has no direction, only magnitude
Rate of change of DISTANCE with respect to time

14. Units What is Measured? Units Symbol Time s, min, hours t Distance
m, km,cm
mi, ft, in d
Displacement
Velocity
m/s, km/hr
mph v

15. Quick Checks What is the difference between speed and velocity?
What is the equation for average velocity?
What does it mean for motion when velocity is positive?
Units for time? Distance? Displacement? Velocity?

16. The GUESS Method Given Unknown Equation Substitute Solve velocity
During football practice, Martin and Jesus run 2.7 miles eastward in 25 minutes. How fast were they running?
Given
Unknown
Equation
Substitute
Solve
2.7 miles = d, 25 minutes = t
velocity
v = d/t
v = 2.7 miles/25 minutes
v = miles/min

17. Position vs. Time Graphs
What is in a position vs. time graph?
X-axis: time (s) that the object is in motion
Y-axis: position (m) of the object in motion
SLOPE of the line = velocity!

18. How to Find Slope Slope = rise = Δy run Δx
= How much your position is changing
How much your time is changing

19. Position vs. Time 20 40

20. What is the velocity between t = 0 and t = 4?
Slope = Δy/Δx
Slope = 20m/4 s = 5 m/s

21. What is the velocity between t =4 and t = 6?
Slope = Δy/Δx
Slope = 0m/2 s = 0 m/s
When an object is at rest, its velocity = 0 so slope = 0

22. What is the velocity between t = 6 and t = 8?
Slope = Δy/Δx
Slope = 20m/2 s = 10 m/s

23. What is the velocity between t = 8 and t = 12?
Slope = Δy/Δx
Slope = -20m/4 s = -5 m/s
Negative velocity means…?

24. The steeper the line, the higher the velocity = faster the object is moving
Where was the velocity greatest? 20 40

25. The steeper the line, the higher the velocity = faster the object is moving

26. Exit Ticket
On a scrap piece of paper, answer the following questions about the graph

27. Exit Ticket
David Ron Beckham
Position (m)
Time (s)
Look at the graph. It shows how 3 runners ran a 100-meter race.
Which runner won the race?
Which runner stopped for a rest?
How long did he stop to rest?
How long did Ron take to complete the race?
What is David’s average speed?