1. Kinematics Introduction to Motion

2. Mechanics = Kinematics + Dynamics
The branch of physics dealing with the study of motion.
This comprises about 70% of the AP Physics 1 course, and it is the 1st semester of any college physics program. The information learned in mechanics is used extensively in other areas of physics and is essential base knowledge for physical science majors in college (engineering, physics, chemistry, etc.)
Kinematics
The mathematics of motion, but without regarding the cause of motion.
Linear kinematics will be the first unit in this course, and rotational kinematics will be taught at the start of second semester.
Dynamics
The study of the cause of motion (force and torque).
Linear dynamics will be addressed in the second unit in this course, and rotational dynamics will be taught at the start of second semester.

3. Objectives Define the following Motion Trajectory Particle model
Position
Coordinate
Displacement
Time interval
Uniform motion
Velocity
Explain how motion problems are oriented
Interpret motion diagrams
Distinguish between position, distance, and displacement
Distinguish between speed and velocity
Solve problems involving speed and velocity

4. Defining the terms listed in the previous objective
The following terms can be found in the assigned reading
Motion
Trajectory
Particle model
Position
Coordinate
Displacement
Time interval
Uniform motion
Velocity
Note:
Throughout the course the PowerPoint presentations associated with each assignment will supplement the reading assignments, but not replace them entirely.

5. Orienting Motion Problems
The motion of objects involves several variables
Initial position (location)
Initial speed
Initial direction of motion
Final position
Final speed
Final direction of motion
Changes in these quantities as time passes
As a result, it is important to orient all types of motion in a consistent way.
This requires a specific frame of reference that allows the above values to be visualized and mathematically quantified, and we already have such a device.
The coordinate axis system

6. Setting the Origin of the Coordinate Axis System
The coordinate axis origin (0, 0) can be placed at any location.
In some problems the origin is identified in the problem.
Example: At the start of the problem a car is 100 m to the left of a stop light and the problem asks for it location relative to the stop light after a specified time interval. In this case it makes sense to set the origin at the stop light, since all distances are measured from this location.
In most problems the origin is not identified.
In these problems the starting location of the moving object is the best location to set as the origin of our coordinate axis system.
As a result, the initial location of an object has a zero quantity. This is useful since zero quantities simplify the physics equations we will soon be learning.

7. Determining Direction Along Axes
Once the origin has been set the subsequent direction of motion can be specified using the common language, specifying an axis, and/or as an angle in degrees.
270o or −y
90o or +y
180o or −x
0o or +x IV
III
− angles II
+ angles I
Horizontal Motion: Right +x-direction 0o
Left x-direction 180o
Vertical Motion: Up +y-direction 90o
Down y-direction 270o  90o
Diagonal Motion: Must be specified with degrees, usually from the +x axis

8. Determining Direction Using Reference Angles
A REFERENCE ANGLE is a an angle measured in specified direction from a specified (referenced) axis. D C B A
A: 30o above or counterclockwise from the +x axis
B: 30o above or clockwise from the x-axis
60o left or counterclockwise from the +y-axis
C: 30o below or counterclockwise from the x-axis
60o left or clockwise from the y-axis
D: 30o below or clockwise from the +x-axis
60o right or counterclockwise from the y-axis
The same direction can be described in many ways using reference angles.

9. Determining Direction From the +x Axis
If no reference axis is specified, then the given angle is assumed to have been measured from the +x axis.
Positive angles are counterclockwise (following the numbering of the quadrants)
Negative angles are clockwise D C B A
A: 30o B: 150o C: 210o D: 330o or 30o
We not only control where the coordinate axis origin is set, but also how the entire system is oriented. Since it is easier to work with +x values the coordinate axis system is most often oriented so that objects move initially in the +x direction. As a result, initial motion is most often directed in the 1st and 4th quadrant.
In the 1st quadrant measuring positive angles from the +x axis is obvious.
In the 4th quadrant using negative angles from 0o to 90o in more convenient than measuring counterclockwise all the way around and working between 270o to 360o.

10. Describing and Quantifying Motion
A car in uniform motion travels 300 meters in 6 seconds.
Describe and quantify every detail of this motion. Seems deceptively simple.
Begin by visualizing a car.
But how should it be oriented?
Unfortunately very little information was given.
We need to make some assumptions.
Since no hills were mentioned, assume the car is driving on level ground.
We will also assume there is no air resistance and no friction in all motion problems until these are specifically mentioned.
Let’s set the location of the car when the problem begins as the origin of our coordinate axis system.
In order to work with positive numbers lets set the initial motion of the car to the right along the +x axis.

11. Describing and Quantifying Motion
A car in uniform motion travels 300 meters in 6 seconds.
100
200
300
x (m)
Sadly the actual car is not necessary in the solution of this problem.
For simplicity the car can instead be modeled as a point mass at the origin at the start of the problem.

12. Describing and Quantifying Motion
A car in uniform motion travels 300 meters in 6 seconds.
100
200
300
x (m)
A model is a simplification that focuses on the most important information that is being examined.
Models may bear no resemblance to actual reality, but they make complex thing easier to track and visualize.
Many mathematical aspects of physics treat extended objects as though they are a single point particle located entirely at the object’s center (center of mass).
Modeling the car as a particle oriented on a coordinate axis, lets identify some of the quantities relevant to the motion described above.
The problem describes a car traveling 300 meters. What does this look like?

13. Describing and Quantifying Motion
A car in uniform motion travels 300 meters in 6 seconds.
100
200
300
x (m) xi xf x
Initial Position
Coordinate location at the start of the problem
xi = 0 m
Final Position
Coordinate location at the end of the problem
xf = 300 m
Displacement
Change () in position (x) during the problem. Includes direction (+x) by specifying x and +300.
x = xf  xi x = 300 m
Distance
Distance moved, without specifying direction. Always a positive value regardless of motion.
d = 300 m
Elapsed time
The time interval during the motion.
t = 6 s

14. Motion Diagram
A car in uniform motion travels 300 meters in 6 seconds.
100
200
300
x (m)
The motion can also be broken down into equal time intervals and the position of the car can be shown at each instant of time.
This type of diagram is a motion diagram.
The motion shown above depicts the car’s location every second during the motion.
In this diagram it can be seen that the car travels 50 meters every 1 second.
Which leads us into calculations of speed and velocity.

15. Rates
A car in uniform motion travels 300 meters in 6 seconds.
Rate: A ratio of the change in one variable compared to the change in another variable.
There are many different rates.
However, in motion problems rates are a ratio of the change in a specific variable compared to the elapsed time t .
Essentially when the word “rate” is used in a motion problem it means that the variable mentioned in conjunction with the word rate should be divided by t .
Speed is the rate that distance is travelled
Velocity is the rate of displacement v = t d v = t x

16. What is the difference? v = d v =
A car in uniform motion travels 300 meters in 6 seconds.
Distance and speed are the numerical value only and give no information about direction traveled. The numerical value is known as magnitude.
Displacement and velocity give the numerical value (magnitude) and include the direction traveled.
For motion in a straight line the equations for speed and velocity solve for the same value. As a result, speed is often referred to as the magnitude of velocity.
Speed is the rate that distance is travelled
Velocity is the rate of displacement v = t d v = t x

17. Calculating Speed and Velocity
A car in uniform motion travels 300 meters in 6 seconds.
Speed
Velocity
Which matches the rate seen during every second in the previous motion diagram
100
200
300
x (m)
In this diagram it can be seen that the car travels 50 meters every 1 second.

18. Describing and Quantifying Motion
At first glance this seemed very simple. However, a detailed picture involved:
Making several common assumptions since the problem statement was vague
Simplifying the motion by modeling the car as a particle
Orienting the car’s motion on a coordinate axis
Deciding on a location of the origin
Deciding on a direction of original motion
Determining initial and final positions
Determining the distance and displacement
Calculating the speed and velocity
Viewing the problem as a motion diagram
All of these tools are not necessary in every problem, and may have seemed over the top for this problem. However, problems will be getting more complicated and will require a variety of skills, including a few more. Such as:
Determining initial velocity, final velocities, and acceleration
Identifying hidden zero quantities
Displaying the motion in a table
Graphing the motion several different ways