1. Unit 3: One Dimensional Kinematics

2. Section A: Velocity and Acceleration
Corresponding Book Sections:
2.2, 2.4
PA Assessment Anchors:
S11.C.3

3. What is kinematics? Kinematics
The study of motion and how to describe it
Does not consider what causes the motion
One Dimensional (1D) Kinematics
Motion in a straight line
Left/right, up/down, east/west, etc

4. Coordinate system Defines position of an object Indicates the positive
direction + xf xi
x = 0

5. Basics of a coordinate system
Establish a positive direction
Establish an origin (0 point)
The origin and positive direction must remain the same for the entire problem

6. Sample Problem Page 17, Figure 2-2 Set up a coordinate system
Choose your own origin
Choose the positive direction

7. Distance vs. Displacement
Total length of travel
Units: m, cm, mm, km
Displacement
Change in position = final - initial
x = xf - xi
Greek letter “delta”…stands for “Change in”

8. Back to the sample problem…
Page 17, Figure 2-2
If you leave your friend’s house, go to the supermarket, and come home, find the:
Distance
Displacement

9. Another example…
Suppose you leave the grocery store, stop at your house, go back to the grocery store, and then go to your friend’s house. Find the:
Distance
Displacement

10. Last example…
Suppose you walk from the grocery store to your friend’s house. Find the:
Distance
Displacement

11. What does the negative mean?
Remember that we set a certain direction as positive…
Getting a negative simply means that we are in the opposite direction as the one we established as positive
This DOES NOT mean that a negative number is less than a positive value

12. Before we go any further…
We need to consistently set up problems to make sure we’re following the right steps and make our work clear
(And to receive full credit )

13. Sample Problem Setup Sketch of the Problem All Work Equations Used
Step by-step derivations
(Not division, multiplication, etc)
Data Table
Values
Unknown Variables
Ex:
t = 3s
xi = 5 m
xf = ?

14. It takes practice…
It will take practice to start setting up problems (and not just jumping in to solving them)
In the end, you’ll be more accurate
You MUST set up problems like this on ALL tests, homework assignments, classwork, etc to receive full credit!

15. Speed vs. Velocity Speed Rate of motion Units: m/s, km/hr Velocity
Displacement per unit of time
Units: m/s, km/hr
WITH a direction
N, S, E, W, etc
+ or --

16. Sample Problem
You drive 4.0 hr at 30.0 mph and then another 4.0 hr at 50 mph. Is your average speed:
Greater than 40 mph
Equal to 40 mph
Less than 40 mph

17. Find average speed for each part and average velocity for trip
t = 10 s
t = 50 s

18. Position vs. Time Graph

19. Practice problem #1
Draw a position vs. time graph for the following situation:
You walk 2 m from your house in 3 seconds
You walk another 3 m in 5 seconds
You stop for 4 seconds to rest
You turn around and walk back to your house in 6 seconds

20. Answer…

21. Practice problem #2
Draw a position vs. time graph for the following situation:
You walk 10 m toward the school in 5 seconds
You stop to answer your phone for 10 seconds
You walk back to your car in 5 seconds
You’re late for 1st pd, so you walk to the 10 m to school in 3 seconds.

22. Answer…

23. Instantaneous Speed & Velocity
Instantaneous Velocity
Velocity at one instant in time
Unit: m/s
Instantaneous Speed
Magnitude of the instantaneous velocity

24. Speedometer Question What does a car’s speedometer measure?
Average Speed
Average Velocity
Instantaneous Speed
Instantaneous Velocity
Explain.

25. Acceleration
The change of velocity with time
Units: m/s2, mph/s, etc…

26. Practice Problem #1
Saab advertises a car that goes from 0 to 60 mph in 6.2 seconds. Find the average acceleration.

27. Practice Problem #2
An airplane has an average acceleration of 5.6 m/s2 during takeoff. How long does it take for the plane to reach a speed of 150 mph?

28. Acceleration vs. Deceleration
Final speed > Initial Speed
Deceleration
Final speed < Initial Speed

29. Connection between acceleration and velocity
Situation 1:
Acceleration and velocity in same direction
Speed of object increases
Situation 2:
Acceleration and velocity in different directions
Speed of object decreases

30. Practice Problem #1
A ferry makes a short run between two docks. As the ferry approaches the dock (positive x-direction), it has a speed of 7.4 m/s and slows down to a stop in 12.3 s. Find the acceleration.

31. Practice Problem #2
The ferry now leaves the dock As the ferry approaches the dock, it has a speed of 7.3 m/s and now slows down to a stop in 13.1 s. Find the acceleration.
Hint: Think about positive/negative
direction based on last problem

32. The most important acceleration…
Recall from other science classes that gravity is always pulling down on everything.
Gravity has an acceleration represented by: g
g = 9.8 m/s2
You need to use this exact value

33. Section B: Kinematics Equations
Corresponding Book Sections:
2.5, 2.6, 2.7
PA Assessment Anchors:
S11.C.3

34. Motion with Constant Acceleration
Object is either speeding up or slowing down
Object is just speeding up / slowing down at a constant rate (same acceleration at all times)

35. Kinematics Equations Velocity as a function of time:
Position as a function of time:
Velocity as a function of position:

36. How do I know when to use each equation?
That’s where the sketch and data table will come in handy…
Look at what you have, what you’re looking for, and find the equation that will include all of those variables
You may need to use more than one equation in a problem

37. Practice Problem #1
A ball is thrown straight upward with an initial velocity of 8.2 m/s. If the acceleration of the ball is that of gravity, find the velocity after:
0.50 s
1.0 s

38. Practice Problem #2
A boat moves slowly inside a marina with a constant speed of 1.50 m/s. As soon as it leaves the marina, it accelerates at 2.40 m/s2. Find the:
Speed it’s moving after 5.0 s
Distance it’s traveled after 5.0 s of acceleration

39. Practice Problem #3
A drag racer starts from rest and accelerates at m/s2. How far has it traveled in:
1.0 s
2.0 s
3.0 s

40. Review of the Equations…

41. Freely Falling Objects
Free Fall -- the motion of an object falling only under the influence of gravity.
An object is in free fall the moment it is released, whether it’s thrown upward, downward, or just dropped.
Why don’t we have true free fall on Earth?

42. Consider…

43. More on gravity Remember… That value will be:
Acceleration due to gravity = g = 9.81 m/s2
That value will be:
Positive if our coordinate system has set down as positive
Negative if our coordinate system has set up as positive
Gravity ALWAYS acts in the downward direction. + +

44. Free fall from rest

45. Projectile Motion