1. Linear Motion

2. Defining the important variables

3. Defining the important variables
Kinematics is a way of describing the motion of objects without describing the causes. You can describe an object’s motion:
In words Mathematically Pictorially Graphically
No matter HOW we describe the motion, there are several KEY VARIABLES that we use.
Symbol
Variable
Units t
Time s a
Acceleration
m/s/s
x or y
Displacement m vo
Initial velocity
m/s v
Final velocity
g or ag
Acceleration due to gravity

4. Distance : How far something travels
It is a scalar quantity. It has magnitude but no direction

5. Displacement
Displacement: How far something travels in a given direction
It is a vector quantity because it has both magnitude and direction

6. The SI Unit for distance and displacement is the meter. (m)
SI Units
The SI Unit for distance and displacement is the meter. (m)

7. Speed Notes
IV. Speed
A.        Speed is a quanitative measure of the rate of motion or a measure of how fast an object moves.

8. B.        Speed is calculated by recording distance covered over a period of time:
S = d t

9. t = d or d = St S

10. Velocity
C.        Velocity is speed in a given direction. Therefore:
v = d t

11. Instantaneous Velocity
D.        Instantaneous Velocity – velocity at any given point.

12. Constant Velocity
F.        Constant Velocity - Maintaining velocity over a period of time.

13. Average Velocity
G.        Average Velocity – Average of velocities over a period of time.

14. Example #1
Ben watches a thunderstorm from his apartment window. He sees a flash of a lightening bolt and begins counting the seconds until he hears the clap of thunder 10.0s later. Assume that the speed of sound in air is m/s
How far away was the lightening bolt in a) in m? b) in km?

15. Example #2
On May 29,1988, Rick Mears won the Indianapolis 500 in 3.4h. What was his average speed during the 500 mi race?
(Note: Generally the unit ‘miles’ is not used in Physics exercises. However, the Indianapolis 500 is a race that us measured in miles, so the mile is appropriate here. Don’t forget, the SI unit for distance is the meter.)

16. Example # 3
The slowest animal ever discovered was a crab found in the red Sea. It traveled with an average speed of 5.7 km/y.
How long would it take this crab to travel 100 km?

17. Example #4
Tiffany, who is opening in a new broadway show, has some limo trouble in the city. With only 8 minutes until curtain call, she hails a cab and they speed off to the theatre down a 1000 m long one-way street at a speed of 25 m/s. At the end of the street the cab drives waits at a traffic light for 1.5 min. and then turns north onto a 1700 m long traffic filled avenue on which he is able to travel at a speed of only 10 m/s. Finally this brings them to the theatre.

18. Example #4 (con’t)
Does Tiffany arrive before the theatre lights dim?
Draw a distance time graph of the situation.

19. Graph
Distance vs. Time
3000
2000
1000
Segment 1 Distance of 1000 m covered in short time, cab has high speed shown on a steep slope.
Segment 2 Cab is at rest but time continues to pass
Segment 3 Distance of 1700m covered in larger amt of time cab travels slowly.
Time (s)
Slope is not steep.

20. Acceleration  
A.       The rate at which velocity changes over the time interval during which it occurred.

21. B. Equation a =  v = vf - vi  t tf - ti
Greek Symbol meaning ‘change of’
Vf subscript

22. D.       When acceleration increases its’ change is positive thus the acceleration is positive; when acceleration decreases its’ change produces a negative value.

23. E.       Acceleration is the slope of a velocity - time graph
slope = rise = v = a
run t

24. F. Acceleration that does not change in time is uniform or constant acceleration. In this case, the velocity time graph is a straight line

25. H.       Average acceleration is acceleration measured over a finite time interval.

26. G.       Instantaneous acceleration is acceleration at a specific time; slope tangent to velocity time graph.

27. H.       Average acceleration is acceleration measured over a finite time interval.

28. Example # 1
Grace is driving her sports car at 30 m/s when a ball rolls out into the street in front of her.
Grace slams on her brakes and comes to a stop in 3 s. What was the acceleration of Grace’s car?

29. Kinematic #1
Example: A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m/s/s.
a) How fast is the boat moving after accelerating for 5 seconds?
What do I know?
What do I want?
vo= 1.50 m/s
v = ?
a = 2.40 m/s/s
t = 5 s
13.5 m/s

30. Kinematic #2
b) How far did the boat travel during that time?
37.5 m

31. Does all this make sense?
13.5 m/s
1.5 m/s
Total displacement = = 37.5 m = Total AREA under the line.

32. Interesting to Note A = HB
Most of the time, xo=0, but if it is not don’t forget to ADD in the initial position of the object.
A=1/2HB

33. Acceleration with distance

34. The displacement of an object in a given amount of time
Δd = vo Δ t + ½ a Δt2
If vo = 0 then
Δd = ½ a Δt2

35. Kinematic #3
Example: You are driving through town at 12 m/s when suddenly a ball rolls
out in front of your car. You apply the brakes and begin decelerating at
3.5 m/s/s.
How far do you travel before coming to a complete stop?
What do I know?
What do I want?
vo= 12 m/s
x = ?
a = -3.5 m/s/s
V = 0 m/s
20.57 m

36. Common Problems Students Have
I don’t know which equation to choose!!!
Equation
Missing Variable x v t

37. Example # 1
Monica is walking to the hairdresser’s at 1.3m/s when she glances at her watch and realizes that she is going to be late for her appointment. She gradually quickens her pace at a rate of .09m/s2
What is Monica’s speed after 10s?
B) At this speed, is Monica walking or jogging or running very fast?

38. Example #2
A torpedo fired from a submarine is propelled through the water with a speed of 20 m/s and explodes upon impact with a target 2000m away. If the sound of the impact is heard 101.4s after the torpedo was fired, what is the speed of sound in the water?