(New) AP Physics 1 - Unit 1 Review - Kinematics - Exam Prep

Summary

This Flipping Physics review covers key concepts of AP Physics 1's Unit 1: Kinematics. It starts with a brief discussion on significant figures and unit conversions, emphasizing their relevance in physics. The review then delves into the differences between vectors and scalars, using examples like displacement and velocity for vectors, and mass and energy for scalars. It explains the representation of vectors, displacement, and the distinction between speed and velocity. The segment also touches on acceleration, uniformly accelerated motion equations, and free fall. The review continues with motion graphs, two-dimensional motion, projectile motion, and concludes with relative motion, providing a comprehensive overview of kinematics for AP Physics 1 students.

Takeaways

• 🔢 The AP Physics 1 exam typically disregards significant figures, suggesting that using approximately 3 significant figures is sufficient.
• 🔄 Understanding unit conversions is crucial for grasping physics concepts, such as converting kilograms per cubic meter to grams per cubic centimeter.
• 📏 Vectors are quantities with both magnitude and direction, exemplified by displacement, velocity, and force, while scalars like time and mass have only magnitude.
• 🧭 Vectors can be denoted by an arrow over a variable, a subscript, or by boldfacing, with the understanding that boldface might not be visible on the AP exam.
• 📉 Displacement, represented as delta x, is the straight-line distance from an object's initial to final position, and it is a vector quantity.
• 🚀 Average speed is a scalar calculated as total distance traveled divided by time, whereas average velocity, a vector, is the displacement divided by time.
• ⏱️ Instantaneous velocity and acceleration are specific time-point measurements, differing from average calculations which consider a time interval.
• 📚 The Uniformly Accelerated Motion (UAM) equations, also known as kinematics equations, are essential for solving physics problems with constant acceleration.
• 📈 In motion graphs, the slope of a position versus time graph represents velocity, and the area under a velocity versus time graph signifies change in position.
• 🌐 Projectile motion involves separating motion into horizontal (constant velocity) and vertical (free fall) components, simplifying the problem-solving process.

Q & A

What is the significance of significant figures in AP Physics 1 exams?

The AP Physics 1 exam pretty much ignores significant figures, so it is suggested to ignore them as well, as long as roughly 3 significant figures are used.

How do you convert kilograms per cubic meter to grams per cubic centimeter?

You multiply by 1000 grams over 1 kilogram and then by 1 meter over 100 centimeters cubed, which results in 8.77 grams per cubic centimeter.

What are the differences between vectors and scalars in physics?

Vectors have both magnitude and direction, while scalars have magnitude but no direction.

What are some examples of vectors in physics mentioned in the script?

Examples of vectors include displacement, velocity, acceleration, force, momentum, torque, and angular momentum.

What are some examples of scalars in physics mentioned in the script?

Examples of scalars include time, distance, mass, speed, volume, density, work, energy, and rotational inertia.

How are vectors typically represented in diagrams?

Vectors are often illustrated using arrows, with the length of the arrow representing the magnitude of the vector.

What does displacement represent in physics?

Displacement represents the straight-line distance between the initial and final locations of an object, or the change in position of an object.

How is average speed different from average velocity?

Average speed is the total distance traveled divided by the time taken, while average velocity is the displacement divided by the time interval.

What are the typical units for velocity and speed?

Typical units for velocity and speed are meters per second, kilometers per hour, or miles per hour.

What are the Uniformly Accelerated Motion (UAM) equations also known as?

The UAM equations are also sometimes called the kinematics equations.

What are the five UAM variables?

The five UAM variables are acceleration, velocity final, velocity initial, displacement, and change in time.

How does the slope of a position versus time graph relate to the motion of an object?

The slope of a position versus time graph represents the velocity of the object, indicating how the position of the object changes over time.

What is the significance of the area between the curve and the time axis on a velocity versus time graph?

The area between the curve and the time axis on a velocity versus time graph represents the change in position of the object.

How is free fall motion described in the context of the script?

Free fall motion is described as the motion of an object where the only force acting on it is gravity, resulting in a constant acceleration downward.

What is the typical approach for solving projectile motion problems as described in the script?

The typical approach for solving projectile motion problems is to separate known values into x and y-directions, considering constant velocity in the x-direction and free fall motion in the y-direction.

How does relative motion affect the description of an object's motion?

Relative motion means that the description of an object's motion changes depending on the frame of reference of the observer, often involving vector addition along one dimension.

Outlines

00:00

📚 Introduction to AP Physics 1: Kinematics Review

The script begins with a review of Unit 1: Kinematics for AP Physics 1, focusing on significant figures and conversions. The instructor advises students to disregard significant figures for the exam, suggesting a rough estimate of three significant figures is sufficient. A conversion example is provided, converting 8,765 kilograms per cubic meter to grams per cubic centimeter, emphasizing the importance of understanding conversions in physics. The review then transitions into discussing vectors and scalars, their properties, and examples, with vectors having both magnitude and direction, and scalars having only magnitude. The script also covers the representation of vectors in diagrams and the concept of displacement as a vector quantity.

05:03

🔍 Deep Dive into Kinematic Concepts

This section delves deeper into kinematic concepts, starting with the definitions and equations of average speed and average velocity, highlighting the difference between the two as speed being a scalar and velocity a vector. The discussion continues with acceleration, explaining it as a vector and providing the typical unit of measurement. The concept of uniformly accelerated motion (UAM) equations is introduced, and the instructor presents an additional helpful equation. The UAM variables are listed, and the script clarifies the use of these variables in equations, emphasizing the directional nature of these variables.

10:04

📉 Analyzing Motion Graphs and Free Fall

The script explores motion graphs, explaining the significance of the slope and the area under the curves in position versus time and velocity versus time graphs. It clarifies that the slope represents velocity in the former and acceleration in the latter. The area under the velocity versus time graph is identified as the change in position, while the area under the acceleration versus time graph represents the change in velocity. The discussion then moves to free fall motion, where the only force acting on an object is gravity, leading to a constant acceleration. The script advises using the UAM equations for such scenarios and provides guidance on handling square root calculations in the context of these equations.

15:06

🚀 Exploring Two-Dimensional Motion and Projectile Motion

This part of the script addresses two-dimensional motion, specifically the process of resolving vectors into their component vectors. An example is given to demonstrate how to break down a vector into its x and y-direction components using sine and cosine functions. The concept of projectile motion is then introduced, where the object moves in two dimensions with gravity as the sole acting force. The approach to solving projectile motion problems involves separating the motion into x and y-directions, with the x-direction experiencing no acceleration and the y-direction undergoing free fall. The script also discusses how to handle the initial velocity components and the symmetry in time for the ascent and descent of the projectile.

20:07

🔄 Understanding Relative Motion

The final section of the script tackles the concept of relative motion, explaining how the description of an object's motion can vary depending on the observer's frame of reference. A scenario involving two cars moving in the same direction is used to illustrate vector addition in the context of relative motion. The script clarifies that the velocity of one car relative to the other can be found by subtracting the velocities of the two cars as measured by a stationary observer. The summary concludes with a reminder that the AP Physics exams simplify significant figures and a note on the Ultimate Review Packet for AP Physics 1, which was previously mentioned in the script.

Keywords

💡Significant Figures

Significant figures, often abbreviated as 'sig figs', refer to the number of significant digits in a number, which indicates the precision of the value. In the context of the video, the instructor suggests that students can generally ignore significant figures for the AP Physics 1 exam, as long as they use approximately three significant figures. This advice simplifies calculations and focuses on the broader understanding of physics rather than the precision of each measurement.

💡Conversions

Conversions in physics involve changing a physical quantity from one unit to another. The video emphasizes the importance of understanding conversions for grasping fundamental physics concepts. An example given is converting kilograms per cubic meter to grams per cubic centimeter, which demonstrates the application of conversion factors and the cancellation of units in calculations.

💡Vectors

Vectors are quantities that have both magnitude and direction. In the video, the instructor explains that vectors are represented in physics by displacement, velocity, acceleration, and force, among others. The script uses the example of illustrating vectors with arrows in diagrams, where the length of the arrow corresponds to the vector's magnitude, showcasing the concept's practical application in visualizing motion.

💡Scalars

Scalars are quantities that have magnitude but no direction. The video contrasts vectors with scalars by providing examples such as time, distance, mass, and speed. Scalars are fundamental in describing properties that do not require a directional component, and understanding this distinction is crucial for solving physics problems accurately.

💡Displacement

Displacement is defined as the straight-line distance between the initial and final positions of an object. The video script clarifies that displacement is a vector and emphasizes that it is the change in position, not the path taken. An example used is if someone travels 5 meters north, the magnitude of their displacement is 5 meters, highlighting the concept's relevance in describing motion.

💡Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including direction. The video explains that average velocity is displacement over time, and instantaneous velocity is the velocity at a specific time. The distinction is crucial for understanding motion, especially when analyzing changes in speed and direction.

💡Acceleration

Acceleration is a vector that represents the rate of change of velocity with respect to time. In the video, it is mentioned that average acceleration equals the change in velocity over time, and it is a key concept in understanding how objects speed up or slow down. The video also touches on the idea of instantaneous acceleration, which is the acceleration at a specific moment.

💡Uniformly Accelerated Motion (UAM) Equations

The UAM equations, also known as kinematics equations, are used to describe the motion of an object when the acceleration is constant. The video script mentions that these equations are provided on the AP Physics 1 exam equation sheet and are essential for solving problems involving constant acceleration. The equations relate variables like acceleration, final and initial velocities, displacement, and time.

💡Free Fall

Free fall motion is discussed in the context of an object near Earth's surface where air resistance is negligible, and the only force acting is gravity. The video script points out that in free fall, the acceleration is constant at 9.81 meters per second squared downward, which simplifies the use of UAM equations for these scenarios. This concept is fundamental for understanding the motion of objects under the influence of gravity alone.

💡Motion Graphs

Motion graphs are graphical representations used to visualize an object's motion. The video explains that the slope of a position versus time graph represents velocity, while the slope of a velocity versus time graph represents acceleration. Additionally, the area under a velocity versus time graph corresponds to the change in position. These graphical tools are essential for analyzing and interpreting motion data in physics.

Highlights

Review of significant figures (sig figs) in AP Physics 1, suggesting to ignore them as the exam mostly does.

Emphasis on understanding conversions as crucial for grasping physics concepts.

Conversion of 8,765 kilograms per cubic meter to grams per cubic centimeter as a tutorial example.

Introduction to vectors and scalars, with examples and their representation in physics.

Explanation of how to identify vectors through notation and diagrams.

Detailed discussion on displacement, its calculation, and its vector nature.

Explanation of the difference between speed and velocity, including their equations and units.

Clarification on the concept of instantaneous velocity versus average velocity.

Description of acceleration, its calculation, and its vector nature.

Introduction to uniformly accelerated motion (UAM) equations and their application.

Discussion on the five UAM variables and their role in solving physics problems.

Explanation of how to use UAM equations when acceleration is constant, like in free fall.

Tutorial on interpreting motion graphs, including position vs. time, velocity vs. time, and acceleration vs. time.

Analysis of how to derive position and acceleration graphs from a given velocity vs. time graph.

Discussion on two-dimensional motion, resolving vectors into their components.

Approach to solving projectile motion problems by separating variables into x and y directions.

Concept of relative motion and how it affects the description of motion based on the frame of reference.

Practical example of calculating relative velocity between two cars moving in the same direction.

Misunderstanding cleared up regarding significant figures and their importance in AP Physics exams.

Transcripts

Good morning! This is my review of  Unit 1: Kinematics, for AP Physics 1. 

♪ Flipping Physics ♪ But actually,  

before we even begin discussing the unit  1 topics, let’s review 2 things. First,  

significant figures, or sig figs. Actually, can we not talk about sig figs? 

Yeah. What? 

Sure. That’s actually my point. The AP  Physics 1 exam pretty much ignores sig figs,  

so I suggest you ignore them as well. As long as  you use roughly 3 sig figs, you should be fine. 

I like it. Yeah. 

Oh man! Second,  

conversions. Understanding how conversions work  does actually help with understanding physics. So,  

let’s do one to make sure you remember  how. Bo, please convert 8,765 kilograms  

per cubic meter to grams per cubic centimeter. Sure. Let’s start by multiplying by 1000 grams  

over 1 kilogram because 1000 grams equals 1  kilogram, therefore 1000 grams over 1 kilogram  

equals 1 and you can multiply anything by 1.  Kilograms cancel out. And now we can multiply by 1  

meter over 100 centimeters because 1 meter equals  100 centimeters. But we have cubic meters in the  

denominator, so we need to cube the conversion  factor. Then we cube everything inside the  

parenthesis and cubic meters cancel out. And that  works out to be 8.77 grams per cubic centimeter. 

Well done Bo, thanks. Also, if you could take  a moment to like this video and subscribe to  

my channel, that would be lovely. And now let’s  begin the unit 1 review in earnest with vectors  

and scalars. Class, vectors have both …? Magnitude and direction. 

And scalars have …? Magnitude but no direction. 

Billy, please give me some  examples of vectors in physics. 

Some examples of vectors are displacement,  velocity, acceleration, force, momentum, torque,  

angular momentum, and those are all vectors. And Bobby, please give me some  

examples of scalars in physics. Examples of scalars are time, distance,  

mass, speed, volume, density, work, energy,  rotational inertia, and that’s all I can think of. 

Thank you both. Now, there are three basic ways  you will see variables identified as vectors;  

an arrow over a variable, a subscript on the  variable, or the variable in boldface. The  

boldface one you probably will not see on the AP  Physics 1 exam, however, it is plausible. Also,  

we often illustrate vectors in diagrams and  illustrations using arrows. The longer the arrow,  

the larger the magnitude of the vector.  For example, if an initial velocity vector  

with a magnitude of 15 meters per second is  illustrated like this, then a final velocity  

vector with a magnitude of 30 meters per second  needs to be drawn with a length which is roughly  

twice as long because 30 meters per second  is 2 times 15 meters per second. Alright,  

next let’s talk about displacement. Billy,  tell me everything about displacement. 

Absolutely! The displacement of an object is  the straight-line distance between the initial  

location of the object and the final location  of the object. In other words, displacement is  

the change in position of an object. A symbol for  displacement is delta x, where x means position  

and delta means change in. Change in position  equals position final minus position initial.  

If the initial and final positions are in the same  location, then the displacement of the object is  

zero, no matter what path the object took to come  back to where it started. That shows that the  

distance an object travels will always be greater  than or equal to the magnitude of the displacement  

of the object. And magnitude just means the amount  of something. For example, if someone travels 5  

meters North, the magnitude of their displacement  is 5 meters. And displacement is a vector. It  

has both magnitude and direction. Wonderful Billy, thanks. Bobby,  

tell me about speed and velocity. Okay. Average speed is the distance  

traveled over the time duration of that travel.  That means the equation is speed equals distance  

over time. But that time in the denominator is  actually the time duration over which the distance  

was traveled, not a specific time. And speed is a  scalar. Average velocity equals displacement over  

change in time. Typical units for velocity and  speed are meters per second, kilometers per hour,  

or miles per hour. And velocity is a vector. Thank you Bobby. I will also point out that,  

if the time interval over which the average  velocity is taken is very small, then the velocity  

is considered to be an instantaneous velocity.  Where an instantaneous velocity is the velocity at  

a specific time, rather than the average velocity  which is the velocity over a time period. Okay,  

Bo, please tell us about acceleration. Sure. Average acceleration equals change  

in velocity over change in time. Acceleration  is a vector. Typical units for acceleration are  

meters per second squared. Actually, that’s all  we really ever see for the units for acceleration.  

And I guess I’ll point out that, if the time  interval over which the average acceleration  

is taken is very small, then the acceleration is  considered to be an instantaneous acceleration.  

Where an instantaneous acceleration is  the acceleration at a specific time,  

rather than the average acceleration which  is the acceleration over a time period. 

Nice. Thanks. 

Yeah. Next, when the acceleration of an object  does not change, when the acceleration remains  

constant or uniform, we can use these uniformly  accelerated motion equations or UAM equations.  

These three UAM equations are the ones provided  on the equation sheet, however, there is one more  

UAM equation I think it is helpful to remember.  That equation is displacement equals one half the  

quantity velocity final in the x-direction  plus velocity initial in the x-direction  

all times time. I will point out that these UAM  equations are also sometimes called the kinematics  

equations. Billy, what are the 5 UAM variables? The 5 UAM variables are acceleration,  

velocity final, velocity initial,  displacement, and change in time. 

I do not see velocity final, displacement, or  change in time in any of those UAM equations. 

Mr.p usually uses change in time instead of  just time in the UAM equations. These equations  

assume time initial is zero. Because change  in time equals time final minus time initial,  

with time initial equal to zero, change in time  equals just time final and the College Board drops  

the final subscript from the variable.  So, change in time equals t for time. 

Oh, yeah, that means velocity with a  subscript of x means velocity final in  

the x-direction. That’s where velocity final is. And position final, or x, minus position initial,  

or x with a subscript of zero, equals  change in position or displacement. 

Right. And the variables are positive or  negative depending on direction. Like a  

final velocity which is down is negative. Unless  you’ve specifically identified down as positive. 

Correct. So, class, there  are how many UAM variables? 

Five. How many UAM equations? 

Four. And, if you know how many of the UAM variables? 

Three. You can figure out the other … 

Two. Which leaves you with one … 

Happy physics student! I love that! 

Yeah. Sure. It is kinda fun. 

It sure is! Yeah! 

Please realize both of the velocities in the UAM  equations are instantaneous. Velocity final and  

velocity initial are both at a specific point  in time, hence instantaneous velocities. Next,  

let’s talk about what happens when an object,  like this ball, is close to the surface of planet  

Earth and air resistance can be ignored.  Bobby, what do we know about this object? 

Uh we know the only force acting on the  object is the force of gravity and that means  

the acceleration of the object is 9.81 meters  per second squared in the downward direction. 

This motion is often called Free Fall. Sure. And, we can actually just use 10  

meters per second squared for the Earth’s free  fall acceleration on the AP Physics exams. An  

object in Free Fall has a constant acceleration,  so we can use the uniformly accelerated motion  

equations. Also, the velocity of the object at  the top of the path in the y-direction is zero. 

And remember, when taking the square root, to  be smarter than your calculator and consider  

if the answer your calculator gives you is  positive or negative. That often comes up  

when we use the UAM equation with the squares  of the final and initial velocities in it. 

Right. Perfect. Thanks everybody. Next,  

let’s talk about motion graphs. Class, what  is the slope of a position versus time graph? 

Velocity. Uh how did delta x go from the first  

denominator to the second numerator? Uh … 

Oh! The delta x in the first denominator  refers to the change in whatever is on the  

x axis and the delta x in the second numerator  refers to the change in position of the object. 

Yeah. We replace the y in the first  numerator with position or “x”,  

because that is what is on the y-axis. And we replace the x in the first denominator  

with time or “t”, because that is what is  on the x-axis. Thanks, that makes sense. 

You are welcome. Class, what is the slope of a  

velocity versus time graph. Acceleration. 

To clarify, slope equals change in what’s on  the vertical axis over change in what’s on the  

horizontal axis. For position versus time, the  slope is change in position over change in time,  

which means the slope is velocity. For  velocity versus time, the slope is change  

in velocity over change in time, which  means the slope is acceleration. Class,  

what is the area between the curve and the  time axis on a velocity versus time graph? 

Change in position. And the area between the curve and the time  

axis on an acceleration versus time graph is …? Change in velocity. 

To clarify, the area between the curve and the  horizontal axis of a graph equals what is on the  

vertical axis times what is on the horizontal  axis. Because the equation for velocity can  

be rearranged to be change in position equals  velocity times change in time, the area between  

the curve and the time axis on a velocity versus  time graph is change in position. And because the  

equation for acceleration can be rearranged  to be change in velocity equals acceleration  

times change in time, the area between the  curve and the time axis on an acceleration  

versus time graph is change in velocity. And remember the area above the horizontal  

axis is positive and the area below the  horizontal axis is negative, right mr.p? 

Absolutely Billy. And I just want to make sure  everyone realizes these three graphs cannot  

all describe the motion of one object.  To illustrate that point, let’s remove  

what is on the position and acceleration versus  time graphs and use the velocity versus time  

graph to build the accompanying position  and acceleration versus time graphs for  

the motion of an object. Bo, tell me what you see. Sure. Well, we know the slope of a velocity versus  

time graph is acceleration. The slope  of this velocity versus time graph is  

a constant, negative value. That means the  acceleration graph should have a constant,  

negative value. That is a horizontal line  which is below the horizontal time axis. 

(That is correct Bo. What about  the position versus time graph?) 

Well, we know the slope of a position versus  time graph is velocity. The initial velocity  

of the object is positive, that means the initial  slope of the position versus time graph should be  

positive. But, where do we start the position  versus time graph? I mean, is that information  

even on the velocity versus time graph? That is a great question Bo. And, no, a velocity  

versus time graph on its own does not give you  any information about the initial position of the  

object. For our purposes today, let’s just assume  the initial position of the object is zero. But,  

again, realize we did not get that from the  velocity versus time graph, we just decided the  

initial position is zero. Bo, please keep going. Okay. We decided the initial position is zero,  

so let’s start the position versus time graph  there. And we know the initial slope is positive  

because the initial value for velocity on the  velocity versus time graph is positive. As time  

increases on the velocity versus time graph the  velocity of the object decreases. That means the  

slope on the position versus time graph decreases.  Halfway through the motion the velocity on the  

velocity versus time graph is zero, that means  the slope of the position versus time curve is  

zero at that point. After that the velocity on the  velocity versus time graph is negative and getting  

more and more negative. That means the slope of  the position versus time curve decreases in value. 

Hold up, we know the area under a velocity  versus time graph is change in position, right? 

Yeah. And? And the area above  

the horizontal axis is positive and the area  below the horizontal axis is negative, right? 

Yeah. And? The positive and negative  

triangular areas between the velocity curve and  the time axis are equal in magnitude. That means  

they add up to zero. That means the displacement  of the object for the whole graph is zero. 

And that is why the final position on the position  versus time graph is zero. The total displacement  

is zero and the initial position is zero.  It goes back to where it started. Nice. 

And the area between the acceleration  curve and the horizontal time axis is  

change in velocity. That whole area is below  the horizontal time axis. That means the change  

in velocity for the object is negative.  Which you can see on the velocity versus  

time graph. Cool. 

Nice. Well done everybody! Now,  

I just want to take a moment to identify  what type of motion this is. Any thoughts? 

Uh … Yeah. 

Well, the acceleration is a constant,  

negative number. … Right. It is free fall motion. 

Oh, as long as that constant acceleration is about  negative 10 meters per second squared, right? 

Actually, if it’s a different number, this could  just be near the surface of a different planet. 

Sure. The initial and final points are the same,  

and the object goes up and then comes down again. And the velocity for the first half is positive  

and for the second half is negative. So, it’s probably an object thrown upward  

near the surface of a planet with negligible  air resistance as long as that object was  

caught at the same height it was thrown. And it’s uniformly accelerated motion. 

Yep. Yeah. 

But it could just be something  with a constant acceleration. 

Yeah. Well done. Yes,  

that is correct. {Phone rings.} I’m  sorry. Give me a sec. I gotta take this. 

Good morning. What do you both  

think of the Ultimate Review Packet? I like it. Seems pretty useful. 

What’s the Ultimate Review Packet? Billy and What’s the Ultimate Review Packet? 

Yeah. What’s the Ultimate Review Packet? The Ultimate Review Packet is only the single  

greatest resource for studying AP Physics  1. It’s got review videos, study guides,  

more review videos, multiple-choice problems,  helpful videos which go over common difficult  

topics in AP Physics 1, a practice AP Physics  1 exam, solutions to free response questions,  

actually, it’s got detailed solutions to  everything in the Ultimate Review Packet,  

and more. It’s awesome! Back me up here Bobby! 

Sure. I’m just trying to figure out how Bo does  not know what it is, considering he’s in it. 

I am? We all are. 

That does not surprise me. Is it free? 

No, it is not free. Mr.p’s got to make money  

somehow. Giving away so much of his content  for free does not really pay the bills. 

Speaking of mr.p. Welcome back. Thanks. And sorry about that. Next up,  

two-dimensional motion. Often, in 2D motion, you  will have to break, or resolve, vectors into their  

component vectors. Bobby, please break this vector  A, which is at an angle theta with the vertical,  

into its x and y-direction components. Okay. Sine theta equals opposite over  

hypotenuse. The side opposite theta is vector  A in the x-direction, and on the hypotenuse  

is vector A. That means vector A in the  x-direction equals A sine theta. Cosine  

theta equals adjacent over hypotenuse. The side  adjacent theta is vector A in the y-direction,  

and the hypotenuse is still vector A. That means  vector A in the y-direction equals A cosine theta. 

I thought the x-direction used  cosine and the y-direction used sine? 

That’s only true when the  angle is with the horizontal. 

Yeah, you really should walk through the equation  each time to make sure you don’t mess it up. I’ve  

messed it up a lot of times. I have too. 

Sure. Thank you. Now,  

projectile motion is where an object is moving  in two-dimensions near the surface of a planet  

with the only force acting on the object being  the force of gravity. Billy, what is a typical  

approach for solving projectile motion problems? When solving projectile motion problems,  

we typically separate our known values into  the x and y-directions. In the x-direction the  

acceleration of the projectile is zero because  there are no forces acting on the projectile  

in the x-direction. That means the velocity of  the projectile in the x-direction is constant.  

And the equation for that is velocity in  the x-direction equals displacement in the  

x-direction over change in time. There are 3  variables in that equation which means if we  

know 2 of the variables we can find the other 1.  In the y-direction the projectile is in free fall  

because the only force acting on the projectile  in the y-direction is the force of gravity. That  

means the acceleration of the projectile in  the y-direction equals negative little g,  

or the negative of free fall acceleration, so  negative 9.81 meters per second squared, however,  

on the AP Physics exams we can just use 10 meters  per second squared to make all the calculations  

easier. In other words, in the y-direction,  the acceleration of the projectile is constant  

and we can use the Uniformly Accelerated Motion  equations. Those have 5 variables and 4 equations,  

which means, if we know 3 of the variables, we  can figure out the other 2, which leaves me! 

Me too. And me. I’m full of mirth. 

The only variable which is the same in both  directions is change in time because change  

in time is a scalar. So, often we are solving  for change in time in one direction and using  

it in the other. Also, we often need to resolve  the initial velocity into its components like you  

just had Bobby do. Unless the initial velocity is  completely horizontal, then the initial velocity  

of the projectile in the y-direction is zero. Oh,  and the velocity of a projectile at the very top  

of its path in the y-direction is zero! And if the projectile starts and ends  

at the same height, in other words the  displacement in the y-direction equals zero,  

then the change in time while going up is the  same and the change in time while going down. 

And the velocity in initial in the y-direction  equals the negative of the velocity final in  

the y-direction, again where the initial  and final points are at the same height. 

Well done y’all. Thanks. Last up we have  relative motion. The basic idea here is that  

the description of the motion of an object changes  depending on the frame of reference of the person  

observing the motion. What? Ehhhh? Uhhh? 

Yeah, I know that sounds complicated. It  really is not. It’s just vector addition and,  

for the purposes of AP Physics 1, they have  stated that relative motion is “restricted  

to motion along one dimension.” Likely, they will  ask you something along the lines of “A stationary  

observer measures car A to be moving at 60 km/hr  East and car B to be moving at 35 km/hr East. What  

would a person in car B measure the velocity  of car A to be?” Bo, please solve this one. 

Sure. We know the velocity of car A relative to  the Earth is 60 km/hr East and the velocity of  

car B relative to the Earth is 35 km/hr East. And  we are solving for the velocity of car A relative  

to car B, because the frame of reference in the  question is the observer who is in car B. Looking  

at it in terms of vector addition, the velocity  of car A with respect to car B plus the velocity  

of car B with respect to the Earth equals the  velocity of car A with respect to the Earth.  

You can see that in the vector addition diagram  and we can remember that the common variable,  

car B, drops out and we are left with car A and  the Earth or the velocity of car A with respect  

to the Earth. .. Solving for the velocity of car  A with respect to car B, we get that that equals  

the velocity of car A with respect to the Earth  minus the velocity of car B with respect to the  

Earth or 60 km/hr East minus 35 km/hr East or 25  km/hr East. If a passenger in car B looks out the  

window as car A passes it, car A will look like it  is moving at 25 km/hr East or forward at 25 km/hr. 

What if the question asks, “What would a person  in car A measure the velocity of car B to be?”  

That really is too many A’s and B’s. Yeah it is. The velocity of car B with  

respect to car A is just the negative of the  velocity of car A with respect to car B. So,  

the velocity of car B with respect to car A equals  negative 25 km/hr East, and negative East is West.  

So, the velocity of car B with respect to car A  equals 25 km/hr West. A passenger looking out the  

window of car A as it passes car B will see car B  moving at 25 km/hr West or backwards at 25 km/hr. 

Should it be 20 km/hr and not 25  km/hr because 60 only has 1 sig fig? 

Nope. Remember the AP Physics exams do not  really concern themselves with sig figs. 

Oh yeah, right. Thanks. Absolutely. Well, that concludes  

my Unit 1 AP Physics 1 review. I do want to take  a moment to let you know about my AP Physics 1  

Ultimate Review Packet. We already did that. 

(We, We did?) While you were on the phone. 

Oh. Right. Well, thank you for that then. You are welcome! 

No problem. Wait a second, was that a real phone call? 

Thank you very much for learning with  me today, I enjoy learning with you.