1-Kinematics (motion)
TextBook: Chapter 1 & 3.5 in in College Physics
Online Drill/review work: https://www.physicsclassroom.com/Physics-Tutorial/1-D-Kinematics
What is in this unit?
Kinematics is the study of motion of objects based of observations of change in position, velocity and acceleration. It does not look at the cause of motion (forces or inertia).
Scenarios involved are either constant speed or constant acceleration scenarios for movement along straight lines as well as projectile motion (when objects move through the air only accelerated by gravity).
Equations
What's not on the formula chart?
Displacement: Δx=x-x0
Average Speed: vavg= Δx / t = (v2 + v1) / 2
Skill: Use graphs to represent motion, solve problems
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
Fact: On a velocity as a function of time graph, slope represents acceleration; speeding up involves moving away from the X-axis.
Skill: calculate area "under the curve", tell what that means, and use that value to solve problems or describe what motion is occurring. Use the video at right 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
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.
How to video for finding area under velocity (time) graph).
If you like this type of video and want more, check out the whole kinematics playlist on YouTube
Skill: Use Kinematics Equations to solve 1D motion problems
Only when motion is uniformly accelerated can use the 3/4 kinematic equations above to determine the speed, position, time or acceleration of the object.
Use the video at right 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 frictionless (no air resistance) free-fall on earth
Practice choosing the right kinematics equation at with this worksheet or these PhysicsClassroom.com Kinematics Practice Problems
General Skills so far
See the general skills pages for info on each of these skills which were introduced in class:
Using multiple representations to re-express key elements of observations. This includes translating between one graph to another or verbal to mathematical or any of these and a diagram.
Use math with literal equations, numerical values, and solve proportion problems. Practice with this worksheet/notes
Design a plan to collect data to answer a scientific question. This includes selecting what to measure, what tools to use, and writing procedures.
Analyze data to identify patterns and relationships. This includes graphing data, verbally describing relationships shown on a graph, identifying the physical meaning of quantities like area and slope of the graph, and using an equation 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.
Model Situations: Projectiles
Assuming air resistance is negligible we can always assume the following for projectiles (airborne objects without motive power)
Fact: free fall motion is defined as motion only accelerated due to gravity (no air resistance; this includes upward motions)
Fact: horizontal motion is unaccelerated (v0x = vx and ax = 0)
Fact: vertical motion is accelerated by gravity (ay = g downward, on earth ay = 10 m/s2 downward)
Fact: the maximum height (for objects that rise) occurs when the velocity on the y axis = 0.
Tip: max height and total time in the air questions usually require 2 setups
Bonus fact: Terminal velocity is when air resistance has increased so much that you fall at a constant speed. This is NOT free fall.
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.
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
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).
Misconception 1: Freely falling bodies can only move downward.
What does free-fall really mean? Can you come up with examples of free fall that are not moving 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 downward acceleration causes its vertical velocity to slow to zero -- that is downward acceleration while traveling upward.]
Misconception 2: Gravity only acts on things when they are falling.
Name some times when this is not true.
answers [gravity is acting on us right now even if we are sitting down, keeping us from flying off the ground]
Misconception 3: Acceleration and velocity are always in the same direction.
What happens if they are opposite each other? What happens if they are 90º to each other?
answers [objects slow down][an object turns while maintaining a constant speed]
Misconception 3: The acceleration of a falling object depends upon its mass. (Heavier objects fall faster than light ones.)
What makes this true for many real-life situations? What conditions do we assume in Physics problems that makes it not true?
Can you show/explain why they fall at the same rate?
Answers: [air resistance effects depend on mass, so when air resistance is present and significant large objects can sometimes fall faster][they should fall at the same rate if objects in freefall experience the same acceleration of 9.8 m/s/s downward and the kinematics equations show us that mass is not a factor once the acceleration is known]
Misconception 4: If velocity is zero, then acceleration must be zero too.
When a ball is thrown upward downward acceleration causes its vertical velocity to slow to zero -- that is downward acceleration while traveling upward. In fact, when the ball is at the top of its arc it is stopped for a single moment in time and is still accelerating 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]
A couple more common mistakes to make sure you don't make:
Two objects side by side must have the same speed. -- No, they could be next to each other while one passes another.
Velocity is a force. No, forces require 2 objects to interact, but a velocity only requires one object to be in motion.
Acceleration is the same as velocity. - No, acceleration is the change in your speed or direction. You can have velocity, but while having no acceleration and can even have acceleration with no velocity (momentarily, at least).
My Handouts/Notes
Examples of graphed motion: https://docs.google.com/presentation/d/1YzeDmEcl2oFB_lidHDtBKDe4RyTCfqJJY2sq9IRSLYQ/edit#slide=id.p
summary of these is attached at the bottom of the page
Video found here: Motion Graph Examples
Other Learning Resources
See Mrs. Twu's page for very extensive resources on Kinematics: https://sites.google.com/site/twuphysicslessons/home/kinematics
She has 29 short videos that include explanations and example problems. She also has a set of practice problems.