1. Electric Current Notes
Motion

2. Electric Current Notes
Motion of What?
To simplify things as much as possible, we will first consider one-dimensional motion (motion along a straight line) of particles (points that can’t spin, rotate, flip, flop, or wiggle around).

3. Describing Motions
We will concern ourselves (for now) with describing motion - kinematics.
We will worry about explaining motion (dynamics) later.

4. Two Simple Motions
In our course, we will be primarily concerned describing with 2 simple motions:
Motion with constant velocity
Motion with constant acceleration

5. Electric Current Notes
Position
Mark a zero point on the line, pick a direction to be positive, and measure from there.
Positions can be positive or negative.
Units of position: centimeters, meters, kilometers, inches, feet, miles, etc.
Common symbol: x

6. Operational Definition
Position, like other physical quantities, is defined by telling how you go about measuring it - not by giving synonyms or descriptive phrases. This is called an operational definition.

7. Positions are Relative
Electric Current Notes
Positions are Relative
Different people can mark the line differently, so they can get different numbers for position.
The position number (and unit) really don’t mean anything until you specify where you marked “0”, and which way you made positive - your frame of reference.

8. Electric Current Notes
Displacement
Displacement = net distance moved or net change in position
Common symbol, d or ∆x
If you move from xo to x, displacement, d = ∆x = x - xo

9. Electric Current Notes
Rates
A rate measures how fast something changes.
In physics, a rate is almost always calculated as a quantity divided by time.
Rate Q changes = change in Q
time for Q to change

10. Electric Current Notes
Speed
Speed is the rate position changes, or the rate distance is covered.
There are two kinds of speed:
Average speed
Instantaneous speed

11. Electric Current Notes
Average Speed
Average speed = distance traveled
Or, average speed = displacement
In symbols, v = d or ∆x
Units of speed: m/s, km/h, mi/h, etc.
time it takes
time t t

12. Electric Current Notes
Instantaneous Speed
Instantaneous speed is what the speedometer says.
It is not measured over a time interval, like average speed.

13. Constant Speed
If an object’s instantaneous speed is always the same value, the object has a constant speed.
In this case, average speed = instantaneous speed

14. Electric Current Notes
Velocity
Velocity = speed + direction
2 kinds of velocity
Average velocity = average speed + direction
Instantaneous velocity = instantaneous speed + direction

15. How Velocity Changes The velocity of an object changes if:
It speeds up, or
It slows down, or
It changes direction.

16. What Velocity Means
An object’s velocity tells you how fast its position is changing.
5 m/s means the object’s position changes by 5 meters each second.
60 mi/hr means that the object’s position changes by 60 mi each hour.

17. Velocities are Relative
Speed and velocity are relative quantities. Different observers, in different frames of reference, can measure different velocities.
You measure speed and velocity by comparing two motions.

18. Electric Current Notes
Acceleration
Acceleration is the rate velocity (not speed) changes.
2 kinds:
Average acceleration
Instantaneous acceleration

19. Electric Current Notes
Average Acceleration
Ave. Accel. = change in velocity
in symbols, a = ∆v
Accelerations are not relative quantities.
time it takes t

20. Units of Acceleration
Since acceleration is a velocity divided by a time, its units are a distance unit divided by 2 time units.
This is commonly written 2 ways:
m/s/s = m/s2
km/hr/s = km/hr.s

21. Constant Acceleration
Electric Current Notes
Constant Acceleration
In many common situations, an object’s acceleration is constant, or at least approximately constant.
In this case:
Average accel. = instantaneous accel.

22. Electric Current Notes
Free Fall
Free fall is motion under the influence of gravity only - no friction or air resistance.

23. Acceleration in Free Fall
Electric Current Notes
Acceleration in Free Fall
The acceleration of an object in free fall is constant.
At the surface of Earth, the free-fall acceleration is about 10 m/s2, or 9.8 m/s2 if you have a calculator (or 32 ft/s2 or 22 mi/hr/s in “English” units).

24. Electric Current Notes
Air Resistance
The effect of air resistance is to slow an object down and/or decrease its acceleration.

25. Electric Current Notes
The End

26. Hooray for graphing
and Mr. King too!!!!

27. d t A B C
Graphing !
1 – D Motion
A … Starts at home (origin) and goes forward slowly
B … Not moving (position remains constant as time progresses)
C … Turns around and goes in the other direction quickly, passing up home

28. Graphing w/ Accelerationd
Graphing w/ Acceleration C B t A D
A … Start from rest south of home; increase speed gradually
B … Pass home; gradually slow to a stop (still moving north)
C … Turn around; gradually speed back up again heading south
D … Continue heading south; gradually slow to a stop near the starting point

29. Tangent Lines t On a position vs. time graph: SLOPE VELOCITY Positived
Tangent Lines t
On a position vs. time graph:
SLOPE
VELOCITY
Positive
Negative
Zero
SLOPE
SPEED
Steep
Fast
Gentle
Slow
Flat
Zero

30. Increasing & Decreasingt d
Increasing
Decreasing
On a position vs. time graph:
Increasing means moving forward (positive direction).
Decreasing means moving backwards (negative direction).

31. Concavity On a position vs. time graph:d
Concavity
On a position vs. time graph:
Concave up means positive acceleration.
Concave down means negative acceleration.

32. Times when you are at “home”
Special Points t d Q R P S
Inflection Pt.
P, R
Change of concavity
Peak or Valley Q
Turning point
Time Axis Intercept
P, S
Times when you are at “home”

33. Curve Summary t d B C A D

34. All 3 Graphs t d v t a t

35. Graphing Tips t v t d Line up the graphs vertically.
Draw vertical dashed lines at special points except intercepts.
Map the slopes of the position graph onto the velocity graph.
A red peak or valley means a blue time intercept.

36. Graphing Tips
The same rules apply in making an acceleration graph from a velocity graph. Just graph the slopes! Note: a positive constant slope in blue means a positive constant green segment. The steeper the blue slope, the farther the green segment is from the time axis. v t a t

37. Real life
Note how the v graph is pointy and the a graph skips. In real life, the blue points would be smooth curves and the green segments would be connected. In our class, however, we’ll mainly deal with constant acceleration. v t a t

38. Area under a velocity graph
“forward area”
“backward area”
Area above the time axis = forward (positive) displacement.
Area below the time axis = backward (negative) displacement.
Net area (above - below) = net displacement.
Total area (above + below) = total distance traveled.

39. Area “forward area” “backward area” t v t
The areas above and below are about equal, so even though a significant distance may have been covered, the displacement is about zero, meaning the stopping point was near the starting point. The position graph shows this too. t d

40. v (m/s)
Area units 12
t (s)
Imagine approximating the area under the curve with very thin rectangles.
Each has area of height  width.
The height is in m/s; width is in seconds.
Therefore, area is in meters!
12 m/s
0.5 s
The rectangles under the time axis have negative heights, corresponding to negative displacement.

41. Graphs of a ball thrown straight upd
The ball is thrown from the ground, and it lands on a ledge.
The position graph is parabolic.
The ball peaks at the parabola’s vertex.
The v graph has a slope of -9.8 m/s2.
Map out the slopes!
There is more “positive area” than negative on the v graph. t v t a t

42. Graph Practice Try making all three graphs for the following scenario:
1. Schmedrick starts out north of home. At time zero he’s driving a cement mixer south very fast at a constant speed.
2. He accidentally runs over an innocent moose crossing the road, so he slows to a stop to check on the poor moose.
3. He pauses for a while until he determines the moose is squashed flat and deader than a doornail.
4. Fleeing the scene of the crime, Schmedrick takes off again in the same direction, speeding up quickly.