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TextBook: Chapter 1, 2 & 4.5 in College Physics Explore and Apply
TextBook: Chapter 1, 2 & 4.5 in College Physics Explore and Apply
Online Drill/review work: https://www.physicsclassroom.com/Physics-Tutorial/1-D-Kinematics
What is in this unit?
What is in this unit?
Kinematics is the study of motion of objects based of observations of change in position, velocity and acceleration over time. It does not look at the cause of motion (forces or inertia). Scenarios studied are typically either constant speed or constant acceleration scenarios for movement along straight lines as well as 2D motion, especially projectile motion (when objects move at a constant speed on one axis and under constant acceleration on the other).
In this unit we also build a foundation of terms and skills we will use throughout the course. You can find more details on these in the Science Practices pages of the website, but this unit we will focus on mathematical processes, diagrams of vectors, designing lab investigations and creating, interpreting, and sketching graphs.
Equations on the formula chart
Equations on the formula chart
Mathematical Definitions
(not on the formula chart)
Mathematical Definitions
(not on the formula chart)
Topic Explanations and Facts
Topic Explanations and Facts
Topic 1.1 Scalars & Vectors in 1D
Topic 1.1 Scalars & Vectors in 1D
See Section 1.5 on p.8, and section 2.2-2.3 starting on 15 in College Physics Explore and Apply.
Scalars are quantities described by magnitude only;
scalar examples include distance, speed, and time
Vectors are quantities described by both magnitude and direction.
Vectors can be visually modeled as arrows with appropriate direction and lengths proportional to their magnitude.
vector examples include position, displacement, velocity, and acceleration
vectors are notated with an arrow above the symbol for that quantity, but the arrow is not needed when analyzing only one dimensional because the sign of the vector component (= or -) completely describes the direction of that component.
Topic 1.2 Displacement, Velocity, and Acceleration
Topic 1.2 Displacement, Velocity, and Acceleration
See section 1.2 on p 5 for modeling, section 2.4 on p 21 for displacement, section 2.6 on p 24 for velocity, section 2.7 on p 30 for acceleration in College Physics Explore and Apply.
Object model concept: All things are made up of smaller bits, but we can usually use simplify this down to a single point at the center of mass and treat it as if all the mass, charge, etc. are all located at this single point. Doing this makes it easier to track the motion of the system of bits. This works well when all the parts move together (like in a car) and when the parts are much smaller than the distanced moved (like a skydiver falling 15,000 ft).
Displacement is the change in an object's position; (final position - initial position)
Average Velocity is the displacement of an object divided by the time interval of the displacement; (displacement/time interval)
Average acceleration is the change in velocity divided by the time interval of the change in velocity (initial velocity - final velocity)/time interval
acceleration includes changes in velocity magnitude and/or direction.
Watch out for a common error: many students think dividing average velocity by time gives acceleration, but it is the change in velocity that is needed.
Instantaneous velocity (the rate of change of an object's position at a given moment) and acceleration (the rate of change of an object's velocity at a given moment) can be approximated by calculating an average for a very small time-interval.
Frequent Scenarios:
constant speed
speeding up from rest or coming to rest from an initial speed
vertical throws upward, downward, and drops from height
Topic 1.3 (part 1) Representing Motion (diagrams and graphs)
Topic 1.3 (part 1) Representing Motion (diagrams and graphs)
For drawing and diagrams see section 2.2 on p15 for motion diagrams, section 2.5 on p 22 for tables and position-time graphs, p 29 for graphing velocity in College Physics Explore and Apply.
For computation see sections 2.8 & 2.9 on p 34 in College Physics Explore and Apply.
Motion can be represented by motion diagrams, figures, graphs, equations, and narrative descriptions.
Motion Diagrams and Figures see 1.A Creating Diagrams for example prompts for motion diagrams, sketching trajectories, and figures to represent vector quantities.
Graphs: when motion is graphed it can be easier to use graphing skills to find the information instead of using the formulas. On other occasions you will be required to show understanding of these graphing processes when you may not be given enough information to solve using equations.
Skill: calculate slope, tell what that means, and use that value to solve problems or describe what motion is occurring
Fact: Slope of a position as a function of time graph represents speed (or velocity); speeding up involves greater magnitude of slope
to find instantaneous velocity find the slope of a line tangent to the point described.
Fact: On a velocity as a function of time graph, slope represents acceleration; speeding up involves moving away from the X-axis.
to find instantaneous acceleration find the slope of a line tangent to the point described.
Skill: calculate area "under the curve", tell what that means, and use that value to solve problems or describe what motion is occurring. Use this physicsclassroom.com video on YouTube to learn the basics to the tricky situations for area under a velocity vs time graphs.
Fact: Area under a velocity as a function of time graph represents displacement; an object is back where it started when there is equal area above and below the axis. See the video at right for how to do this.
Fact: Area under an acceleration as a function of time graph represents change in velocity
Narrative Descriptions
Describe motion in terms of direction of motion (+, -, at rest), velocity (increasing speed, decreasing speed, constant speed, at rest), and acceleration (zero acceleration, positive constant acceleration, constant negative acceleration) from data and graph information.
Practice
Practice
Practice matching position (time), velocity (time) and verbal descriptions with this self-check digital card sort activity.
Practice calculating slope, using proper units, and describing a linear relationship with this worksheet.
Practice giving meaning to slope using this motion mapper game at UniverseAndMore or the physics interactives at physics classroom: Graph That Motion or our Graphs and Ramps or with this printable extra practice worksheet interpreting position and velocity from x and v graphs.
For velocity vs time graphs learn from this web page a physics classroom.
Practice finding area under the curve with this worksheet.
Topic 1.3 (part 2) Representing Motion (calculation)
Topic 1.3 (part 2) Representing Motion (calculation)
For computation see sections 2.8 & 2.9 on p 34 in College Physics Explore and Apply.
Motion can be represented by motion diagrams, figures, graphs, equations, and narrative descriptions.
Kinematics Equations can be used to describe instantaneous linear motion in one dimension as long as acceleration is constant for the time interval being described.
The subscript x is used to indicate that the vector quantities in these equations must all describe components on the same axis (ie. you cannot mix vertical acceleration with horizontal initial velocity).
near the surface of the earth acceleration caused only by the force of gravity is downward, constant and approximately equal to ag = g ≈ 10 m/s2
See skill 2.B Calculating and Estimating for expectations and tips on calculation.
Use this PhysicsClassroom.com video on YouTube to learn how to use kinematics equations, but I suggest altering the steps in the video as shown in purple below to help you prepare for our most challenging skill: derivations.
Identify known values of 3 variables. Write down; relate to the symbols.
(If you cannot find 3, use the assumptions below to figure out others)Identify the unknown. Write it in symbol form.
Find the kinematic equation with those 4 symbols. Write it down.
Substitute any values known to be zero and solve for the unknown in symbol form.
Substitute remaining known values and solve numerically.
Use these common assumptions when it appears not enough info is given:
-being at rest or stopped indicates v=0 (including drops and vertical vy at the top of a throw)
-we often start at a position of 0, but can modify that position to make our work easier.
-ay = gravitational field strength = 9.8 m/s downward in free-fall on earth (free fall means no air resistance, just gravitational effects)
Practice choosing the right kinematics equation at with this worksheet or these PhysicsClassroom.com Kinematics Practice Problems
Review: Before a quiz or test you should try this 2 stage rocket review challenge with a partner. Physics Simulation: Two-Stage Rocket (physicsclassroom.com)
Topic 1.4 Reference Frames and Relative Motion
Topic 1.4 Reference Frames and Relative Motion
See p 14, conceptual exercises 23 & 24 on p 23 & 27 in College Physics Explore and Apply.
The choice of a reference frame will determing the direction and magnitude of measured quantities.
measurements can be converted to measurements from another reference frame by combining the velocity of the object and the velocity of the observer in a given reference frame by addition or subtraction.
the acceleration of any object is the same as measured in all inertial reference frames.
Topic 1.5 Vectors and Motion in 2D
Topic 1.5 Vectors and Motion in 2D
See section 4.5 p 102-107 in College Physics Explore and Apply.
Angled vectors can be resolved into two perpendicular components using a chosen coordinate system and trig functions.
2D motion can be analyzed with 1D kinematics if the motion is separated into components.
While this can technically be tested in any situation, by far the most common scenario is projectile motion. An example of an alternate scenario contrived to meet our goals could be a hockey puck moving at a constant speed on one axis gets a push at regular intervals on the other axis
Model Situations: Projectiles
Model Situations: Projectiles
Projectile Motion is a special case of two dimentional motion that has zero acceleration in one dimension and constant acceleration due to gravity in the second dimension. Free fall motion is defined as motion only accelerated due to gravity (no air resistance; this includes upward motions)
Assuming air resistance is negligible we can always assume the following facts for projectiles (airborne objects without motive power)
Horizontal motion is unaccelerated (v0x = vx and ax = 0)
Vertical motion is accelerated by gravity (ay = g downward, on earth ay = 10 m/s2 downward)
Maximum height (for objects that rise) occurs when the velocity on the y axis = 0.
Max height and total time in the air questions usually require 2 setups
Projectile scenarios to be prepared for:
Vertical free-fall projectiles have no horizontal motion and only the assumptions above
Horizontal launch projectiles have the following assumptions in addition to the general assumptions above:
The initial velocity (muzzle velocity) is ALL on the x axis. (v0y = 0)
The time in the air is only based on height and g
Angled launches on level ground have the following assumptions in addition to the general assumptions above:
The starting and ending positions on the y axis can both be zero
The starting and ending velocities on the y axis are equal, but opposite. (–voy = vy)
In the absence of air resistance, the max height occurs at 1/2 the time of the whole trajectory.
Related fact: Terminal velocity is when air resistance has increased so much that you fall at a constant speed. This is NOT free fall.
Explore these concepts using the projectile motion simulation at Phet, which is embedded below or go through the concept builder activities at pysicsclassroom.com
Practice problem solving solving freefall problems at physicsclassroom.com, horizontal projectiles at physicsclassroom.com and angled launch projectiles at physicsclassroom.com
Science Skills addressed in this unit
Science Skills addressed in this unit
See the Science Practice pages for examples and practice on each of these skills which were introduced in class, but below are some things taught directly in this unit.
Practice 1: Creating Representations
Create a graph of data, including choosing the scale for the axes, labeling the axes, plotting points
Sketch graphs of position, velocity, and acceleration as a function of time based on either other graphs or verbal descriptions.
Represent motion using dot diagrams, trajectories, and vectors of displacement, velocity, change in velocity, and acceleration.
Practice 2: Mathematical Routines
Select an appropriate equation to solve for an unknown from known motion quantities. This includes determining if the situation can be modeled as a constant speed situation or if it is undergoing constant acceleration (needing kinematics).
Derive expressions and analyze the funcational dependance of variables. Calculate numerical responses. Practice with this worksheet/notes
Practice 3: Scientific Questioning and Argumentation
Design a plan to collect data to answer a quesiton about motion of an object. This includes selecting what to measure, what tools to use, and writing procedures that include reducing error through multiple trials and collecting data over a range of manipulated conditions.
Design a plan to analyze data. This includes selectign what to graph, how to linearize data to produce a linear function (in particular, distance and time date or velocity and distance data for accelerated motion).
Analyze data (typically in graphs or tables) to support claims about what the data shows. This includes verbally describing relationships shown on a graph, identifying the physical meaning of quantities like area and slope of the graph, and using derived equations to communicate what the graph shows.
Demonstrate an understanding of measurement error. This includes using a best fit line to reduce random error within a data set, identifying the impact of outliers (blunders) on data, planning to reduce error with data collected across a range of values and multiple trials, and understanding that measurement error means small differences in measured values may still represent the same value so additional data is needed to show a trend continues.
Online Resources for Additional Learning
Online Resources for Additional Learning
Concept builders are self quizzes that progress in difficulty to help you see if you really get a concept. There are several relevant sets of concept builders for this unit:
This website has 2 really great interactive simulations to help you learn. You should check out
Vector Addition: Lean about adding vectors and finding their components.
Projectile Motion: Learn about projectiles, especially about the horizontal and vertical components of the velocity. Also, explore how changing the angle, starting height, and adding air resistance can affect the results.
OPhysics has several really good simulations to help you learn topics for this unit including
several on vectors including addition & vector components
several on translating graphs between x(t), v(t), and a(t)
several on projectile motion, including the monkey and tranquelizer challenge
Ms Twu's has 29 short videos that include explanations, demonstrations, and example problems. She also has a set of practice problems. TwuPhysics at sites.google.com
This playlist has 16 videos with many examples on how to perform many of the functions required in our class. See the whole playlist here:
Mr. P has 32 videos lessons on kinematics that include lecture, demonstrations, and problem solving. The most unique and useful part of his videos is that role played student interactions, which can help you more thoroughly understand the information being taught.
My Handouts/Notes
My Handouts/Notes
Examples of graphed motion: https://docs.google.com/presentation/d/1YzeDmEcl2oFB_lidHDtBKDe4RyTCfqJJY2sq9IRSLYQ/edit#slide=id.p
Misconceptions
Misconceptions
The following are common misconceptions from this unit. It is likely that the AP test will use these as a basis for writing believable distractors in multiple choice questions or look to uncover these in your writing in the free response section. See if you can explain why they are not always true (some are true sometimes, while others are not true at all) and then click the misconception to expand an explanation for that misconception.
Misconception 1: Acceleration and velocity are always in the same direction.
When acceleration and velocity vectors are in the same direction an object speeds up. They can be opposite (causing slowing), perpendicular to each other (causing a change in direction of the velocity), or anything in between (causing a combination of changing speed and turning).
Misconception 2: If velocity is zero, then acceleration must be zero too.
As an example, when a ball is thrown upward acceleration from gravity (downward) causes its vertical velocity to slow and when the ball is at the top of its arc it is stopped for a single moment in time. The acceleration due to gravity is still downward as the moment before its velocity was upward and the moment after the acceleration was downward that means the velocity is actively changing even as the value passes through zero.
Another thing to remember is that acceleration occurs in the direction of unbalanced force, so anytime an object experiences a continuous slowing force and turns around, there will be a velocity of 0 with a non-zero acceleration at the turnaround position.
Misconception 3: Freely falling bodies can only move downward.
Free fall means gravity is the only force acting on an object so it accelerates in a downward direction.
When a ball is thrown upward it slows due only to gravity, so it is in free fall, but is rising.
Misconception 4: We can use a = g = 9.8 m/s^2 for any object that is moving vertically
If there are other forces acting on the object (tension in a string, air resistance, etc) then the object is not in freefall. In these cases, acceleration can only be known by either a) knowing about kinematics evidence (Δv, Δx, Δt) or b) knowing about net force, which we learn in unit 2.
Of course, if the experiment is not done near the surface of the earth (either far away from the surface or near another planet with different gravitational field) you will need to find the gravitational field strength, which we learn in unit 2.
Misconception 5: The acceleration of a falling object depends upon its mass. (Heavier objects fall faster than light ones.)
This is partially true, but often not correct in our course.
It can be true when air resistance is significant. Air resistance is significant when the speed is great enough and the surface area of the object is large for its weight. When that happens, lighter objects will fall with lower acceleration than a heavier object.
On our formula chart there is a phrase that says, "Air resistance is assumed to be negligible unless otherwise stated." So, unless otherwise stated we will assume objects should fall at the same acceleration rate of g downward. This can sometimes be a potential source of error in lab experiments if we see evidence that the acceleration rate was altered in a way that is consistent with air resistance.
Misconception 6: If 2 objects travel the same distance in the same amount of time they have the same speed
Those two objects would have the same average velocity, but speed typically means the magnitude of the instantaneous velocity. So, only if the objects had the same starting velocity and accelerations would traveling the same distance in the same time mean that have the same final speed too.
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