We are constantly in motion and we are constantly surrounded by motion. Whether it’s speeding cars, scampering kittens and even the breeze! Our world is constantly moving even when we sitting down, we are spinning on Earth which is spinning around a sun in a solar system spinning around in a galaxy that is spinning around the universe!

The study of motion and all its varieties is crucial to the study of physics and is mostly considering under the umbrella of kinematics. In order to understand complex motion, we need to understand it’s simplest form which is straight line or linear motion. Let’s think about a rocket launching, blood flowing through a capillary or the trotting horse

How fast is Bowser going? How fast is he going relative to Mario!?!

Let’s talk about reference frames!!

Any measurement of position, distance or speed must be made with respect to a frame of reference.

Ron is traveling on a train which is traveling at 80 kph. Suppose Harry walks past Ron toward the front of the train at 5 kph. This value, 5 kph, is Harry’s speed with respect to the train’s frame of reference. However, with respect to the ground, Harry is moving at his speed with respect to the train plus the train’s speed relative to the ground. That is, to a Hermione, on the ground, Harry is moving, 80 kph + 5 kph = 85 kph.

It is always important to specify the frame of reference when stating a speed. Now, normally, the speed we talk about is relative to the Earth without thinking about it. In the above photo, if Bowser, going 35 kph, passes Mario going 30 kph, Bowser is actually going 5 kph relative to Mario.

When specifying the motion of an object, it is also important to specify the direction of this motion. Direction can be described as North, South, East, West, upwards or downwards to represent a frame of reference. The position of an object in linear motion at any moment is given by the x coordinate of the object. For freely falling objects, we use the y-axis.

It is here where we recognize the difference between displacement and distance. Displacement is defined by the change in position of an object. That is, the displacement is exactly how far an object is from its starting point. To see the distinction between total displacement and total distance, imagine Holly walls 70 m East to a coffee shop and then 30 m West to a park bench to enjoy her cup. The total distance is equal to 100 m. However, since she is only 40 m from her star ing position, her displacement is 70 m – 30 m = 40 m.

Displacement is a quantity with both magnitude and direction. This is called a vector.

The most obvious observation about the motion of a race car, a race horse or a 100 m track racer is how fast they are moving relative to the ground. This is speed and velocity.

Speed refers to how far an object travels in a given time interval, regardless of direction. This is referred to as a rate of change of position and is given in appropriate units for distance and time.

Any speed is defined as the total distance travelled along its path divided by the time it takes to travel that distance.

Speed = distance/time

If Ben travels 240 km in 3 hours, what is his speed?

The terms velocity and speed are sometimes used interchangeably in every day life. Yet, in Physics, we distinguish the two by simply saying speed is a positive number, or the magnitude of velocity. Velocity, on the other hand, signifies magnitude and direction, making velocity another vector! Velocity is, therefore defined in terms of displacement rather than total distance.

Velocity = displacement/time

Is average speed necessarily equal to average velocity??

Nope!!

If Parker Posey walks 40 m East across City Market then walks 30 m West to the Milk section in 70!seconds.

Speed = (40 + 30)/70 = 1.0 m/s

Velocity = (40 – 30)/70 = 0.14 m/s

Questions!!

The position of Wanita as a function of time is plotted moving along the x-axis of a coordinate system. During a 3 second time interval, her position changes from x(1) = 50 m to x(2) = 35 m. What is Wanita’s average velocity.

(x(2) – x(1))/t = (30.5 – 50)/3 = -19.5/3 = -6.5 m/s

The displacement and average velocity are negative indicating Wanita is moving to the left on the axis. Wanita’s average velocity is 6.5 m/s to the left.

How far can Carla travel in 2.5 hours on her bicycle if her average velocity is 18 km/h? We are going to use x = vt.

(a) 18 km/h x 2.5 h = 45 km = 45000 m

According to an Old Wives Tale, every 5 seconds between a lightning flash and the following thunder gives the distance to the flash in miles. Assuming the light arrives in essentially no time at all, estimate the speed of sound in m/s from this rule!

1.609 km/mile x 1 mile/ 5 s x 1000 m/ 1km

= 321.8 m/s, close to 343 m/s!!

We have now begun to delve into the finer points of linear motion with constant velocity!!

To understand constant velocity, we must compare it to something more familiar, speed. Speed is a measure of how Janet or Felicia is moving. Velocity, however, is not another name for speed even though they have the same units. Velocity is the change in position, including direction, divided by the time it took to make that change.

With speed, the length is the distance traveled to the water fountain and back. In velocity, the length is how far and in what direction that point ended up from where it started, i.e. displacement. Therefore, your trip to the water fountain and back leads to a displacement of zero (0)!!

Check out these notes and diagrams that show Position as a function of Time for swimmers, Janet and Felicia!

Average velocity!! Phil runs 50 m in a straight line at 5.0 m/s. Phil then continues to move in the same direction, jogging at 2.0 m/s for an additional 50 m. He then turns around and walks at .80 m/s back to where he started.

(a) Calculate the time spent (1) running (2) jogging (3) walking.

(b) Calculate the average velocity for the (4) run and jog together (5) jog and walk together (6) run, jog and walk together.

🚀 Acceleration!!! 🛬

When an object’s speed or direction of motion changes, that is, whenever it’s velocity changes, we say that an object accelerated or undergoes an acceleration!! Therefore we can say that acceleration is the rate of change in velocity. If Mario’s speed increases 2 m/s every second that means that his acceleration is 2 m/s^2.

So, in many important situations the speed, direction of motion, or both, can change as the object moves. If we look at Mario, game designer added a bit of fire leaving his exhaust which is a solid indication that he has accelerated. Also, we see that he is turning his steering wheel which means he is also accelerating by changing the direction of his motion!!

Acceleration doesn’t have to mean increasing speed!! In everyday language, “acceleration” is used to mean “speeding up” and “deceleration” is used to mean “slowing down”. In our space, however, acceleration refers to any change in velocity and so includes both speeding up and slowing down. Actually, speeding up is accelerating in the direction of motion and slowing down is accelerating in the opposite direction of motion. We will always use the term acceleration to describe any change in velocity!

Now, as you will see in these examples we have a rule and several equations that describe constant acceleration.

🚦Rule 🚦

When an object moving in a straight line speeds up, its velocity and acceleration have the same sign (both positive or both negative). When the same object slows down, it’s velocity and acceleration have opposite signs.

Free Fall

Perhaps the most important case of constant acceleration is the motion of falling objects near the surface of the Earth. Object’s in this category have a constant downward acceleration, if we ignore air resistance.

Free fall is an idealization, but many real life situations embody the concept quite well. Some examples are basketball players leaping for a jump ball, a high diver descending toward the water and a leaping frog in midair. In each case, the falling object experiences minimal air resistance because its speed is relatively slow with a small cross section and falls with a constant downward acceleration.

However a leaf falling toward the Earth or a hawk descending at high speeds with its wings folded, do reach a terminal velocity where the effects of air resistance can no longer be ignored. In this case, the upward air resistance balances the downward force of gravity and the hawk can no longer accelerate!!

Some simple rules!!

1.) An object in free fall has a constant downward acceleration, g, that is equal to 9.8 m/s^2.

2.) the magnitude of this acceleration is the same no matter the size of an object!

3.) This acceleration is the same no matter if the object is moving up, moving down or monetarily at rest!!

4.) For free fall problems, we choose to use the coordinate y instead of x. In this example, we also chose positive y to be upward and and the starting position to be y(o) = 0.

5.) when the object is dropped from rest and falls freely, it travels a greater distance in successive equal time intervals. It accelerates downward.

Acceleration due to Gravity (g)

As we have discussed, the downward force of gravity causes objects that are moving upward or even monetarily at rest to accelerate downward.

If you toss a ball straight up in the air, as it ascends, it’s velocity is positive (upward) and it’s acceleration is negative (downward). Since the velocity and acceleration have opposite signs, the ball slows down. At maximum height, the ball is momentarily at rest so velocity is zero but it is still accelerating because it’s velocity is changing and it’s direction is changing.

If the acceleration at maximum height were equal to zero, the ball would reach this point and then stop in midair!! This does not happen and therefore acceleration is not zero!!

The acceleration due to gravity is always a positive number because it is the magnitude of the acceleration due to gravity. Acceleration is a vector and therefore it is the direction that determines the sign in you chosen coordinate plane. The value of the quantity of g is always positive.

Finally, we can apply the KINEMATICS EQUATIONS to free fall by changing our coordinate plane to the vertical direction, using -g as the acceleration and rewriting the kinematics equations. But first, always remember to Celebrate your Givens!!

Here are some problems that will are great examples of what will be on the test!! These problems build off the lab!!

Acceleration is another one of those palabras that spends time in the realm of the everyday lexicon.

Go faster!! Speed up!! Slow down!! Turn left!!

Each of the above phrases involves an acceleration which essentially is a change in velocity. So we are moving from constant velocity to a change in speed or a change in direction.

This is very important!!

Acceleration is a vector and, just like velocity, it has a magnitude and a direction. So a change in direction is an acceleration the same way an increase or decrease in speed is an acceleration. Therefore, in our vehicles, there are three accelerators, (a) the gas pedal (b) the brake (c) the steering wheel.

So the position 🆚 time graph for an accelerating object is not a straight line. Why?!?! It’s because the slope is not constant as velocity is changing! So let’s delve!! Here is a motion analysis for Jaylene on her scooter going down Pine St.

🚨So we have come up to a rule that will help you throughout the course.🚨

When an object, moving in a straight line, speeds up, its velocity and acceleration have the same sign (+,+ or -,-). When an object moving in a straight line slows down, its velocity and acceleration have opposite signs (+,- or -,+).

So let’s take it up a notch and analyze a world record frisbee catch by one amazing puppy!!

In taking some liberties, here is the golden analysis I came up with and it’s really incredible!!

THE KINEMATIC EQUATIONS

🚨🚨Super Important Notes🚨🚨

The link above ⬆️ will take you to everything you need to know about a special set of equations that apply to motion with constant acceleration, including some very important examples. Like we said, most acceleration in nature is constant.

FREE FALL!!

🚨 Super Important NOTES Part Deux 🚨

And perhaps the most important case of constant acceleration is the motion of objects near the surface of the earth. That is, free fall occurs when only the pull of gravity affects an object’s fall with a constant downward acceleration. Again, it is vital to understand all of the examples and physics speak! Ask questions!

This acceleration due to gravity, g, is the same whether the object is moving up, moving down or even momentarily at rest when it switches directions at its maximum height. Do you think mass affects this acceleration??

Many real life situations come close to this ideal like a high diver descending into the pool or a bullfrog in midair. With relatively low speed, there is minimal air resistance and definitive free fall.

If a falling object, at high speed, has a large cross section, we cannot ignore air resistance. In this case, the motion is no longer free fall because acceleration is not constant. In nature, a hawk plummeting at high speeds reaches its terminal velocity at which the effects of air resistance balances the downward pull of gravity, and therefore can no longer accelerate.

With objects in free fall, we can use the Kinematic Equations in the vertical direction with 9.8 m/s^2 as the constant acceleration due to gravity, or g. On many occasions, it is perfectly acceptable to round to 10 m/s^2 especially in multiple choice situations. So, in the vertical direction, if something is dropped, initial velocity and initial position are both zero, then vertical displacement equation becomes y = 1/2(g)t^2.

The Acceleration due to Gravity or “little g”

The value of g at sea level on earth differs from the acceleration due to gravity on other planets, spacecrafts and even on Mt. Everest!

This is the acceleration due to gravity that affects objects moving upwards, downwards and objects momentarily at rest!!

If we consider upward to be positive and Terry tosses a tennis ball straight up, it has a positive velocity and a negative acceleration. According to our rule, if acceleration and velocity have opposite signs, the ball slows down until the highest point when v = 0 m/s as it stops momentarily to change direction. Acceleration cannot be zero at this point or else the ball would just stop in midair!!! As the ball descends, velocity and acceleration are both negative and the ball speeds up as it falls!!

Projectile Motion

Projectile Motion is the amalgamation of constant horizontal velocity and free fall! In essence, the combination of the ideas that comprise the two sets of notes presented above!! The only force acting on a projectile is the downward pull of gravity!! Here is the Golf Lab and DERIVED EQUATIONS for maximum height of the ball flight and total horizontal displacement and these are universal. This is a great introduction to how we manipulate equations to develop relationships between variables that we are given!!

The water fountain and the leaping ballet dancer each follow a curved path so that their direction is constantly changing. Therefore, we can say that they are accelerating at all points in their motion! But this acceleration is only in the vertical direction so horizontal motion is constant.

For projectile motion, we will always place an axis along the direction of the acceleration due to gravity. Therefore, we can make the direction of the horizontal component of velocity the other axis. So projectile motion is two dimensional motion; motion in a plane. When the ballet dancer leaps, her velocity vector has a horizontal component to the right that remains constant. She also has a velocity vector that points upward which changes due to the acceleration of gravity pulling downwards. An important feature is that the dancer will slow down to zero at her maximum height as quickly as she will speed up on the way down from maximum height. Therefore, corresponding heights in her parabolic arc will have will have the exact same velocity, only a different direction!!!

Let’s play Get the Concept for the changing velocity of a projectile!!

Q: An object launched at some initial speed and angle follows a parabolic arc. At what point during the trajectory is the magnitude of its velocity the smallest? At what point, if any, will the velocity of the object be zero?

A: The magnitude of the velocity is smallest at the peak of its motion. The horizontal component of velocity is constant throughout the trajectory. At maximum height, the vertical (y) component of the velocity is zero (0), so regardless of the magnitude of the horizontal (x) component of velocity, the magnitude of the velocity vector must be the smallest. If the (x) component of velocity is zero, then the tota velocity, both magnitude and direction, is zero (0) at the peak. Because the (x) component of the velocity does not change, horizontal velocity can only be zero if the object was launched straight up!!

So, what do we know about projectile motion?

(1) At maximum height, vertical velocity v(y) is equal to zero.

(2) At maximum height, time (t) is equal to half the total flight time.

(3) Horizontal velocity, v(x), is constant because there is zero (0) horizontal acceleration.

(4) Vertical velocity decreases on the way up, increases on the way down at the same constant rate of 9.8 m/s^2. Sometimes we will round this value to 10 m/s^2 and refer to it as “g”. “g” is always a positive number but generally we call downward the “negative direction”. Therefore, acceleration in the vertical direction a(y) = -g.

(5) We resolve the initial velocity into its vector components and treat both the horizontal and vertical directions ((x) and (y)) as superstar individual problems that we know how to solve using the kinematics equations!!

(6) Time (t) is the same for both directions and cannot be negative and is the bridge between directions.

(7) Since “g” slows things down at the same rate as it speeds things up, vertical velocity (v(y)) is the same at mirroring vertical positions and times during projectile flight.

(8) The magnitude of total velocity is smallest at the peak of motion because the (y) component is zero. If the (x) component is zero, then total velocity is zero. This is a scenario that occurs when a ball is thrown straight up!

(9) We derived the universal derived equations that can be applied to projectile motion!!

FACTOR OF CHANGE!!

Two golf balls are hit from the same point on a flat field. Both are hit it an angle of 30 degrees above the horizontal. Ball 2 has twice the initial velocity of ball 1. Balls 1 and 2 land a displacement d(1) and d(2), respectively, from the initial point. Predict the relationship between the displacements d(1) and d(2), neglecting air resistance.

We will venturing trough these scenarios from the AP workbook in the near future!

What can the Simpsons or any other cartoon teach us about Physics?? I remember my physics teacher, Mitch Johnson, famously saying, “Cartoons are funny because they defy the laws of Physics!” This statement had such a profound influence on me that I wrote an essay to the University of Oxford with it as the theme!

However, we can also learn a lot from proper physics in cartoons as well. The Simpsons are extremely thoughtfully created, living in the balance between physically incorrect scenes and the proper physics we see in the photo! But dare I say that the video has a more of a humorous quality?

Let’s delve into The Simpsons being launched over the sharks! Will the entire family clear the sharks? Why? How can Bart make it across because it looks like he should fall straight down? Well, Matt Groening is a creative genius so he has a few tricks up his sleeve! With the ramp and the water ski rope and handle in the drawing, we are meant to believe that the Marge, Bart, Lisa, Maggie and Homer all took off together with the same speed and were, indeed, all on Homer’s back, maybe?

So, after careful analysis, we can actually consider The Simpsons as projectiles. Projectile motion is defined as motion in two dimensions (2D or Planar) where the only external force on the system is gravity. In these problems we are never really concerned with how the projectile is launched (i.e. kicked, thrown, catapulted, sneezed or hit) as we are with some information as soon as the projectile is in the air, such as the magnitude and direction of the velocity vector.

Since gravity is the only force acting on the Homer and the gang, and gravity is always directed straight down, we know that we can consider motion in this direction to be straight up and straight down. Furthermore, since there are no forces acting in the horizontal direction, we know that the velocity must then remain constant, a concept that will become apparent to you as we get along in the class.

Therefore, by knowing the vector or the components of the vector of velocity, we can predict if and by how much they will avoid the sharks and how far past the sharks they will land!!

Let’s look at a real water ski jump!!!

So, what is Physics??

Some people will try to tell you that it is the study of matter and energy and the interaction between the two. Wait, I missed that because I dozed off!!

I prefer to think of Physics as the Konomi Code to the universe.

Way back in 1985, Kazuhisa Hashimoto was working on the arcade game Gradius. During testing, he developed a shortcut that allowed him to get to where he needed to without dying. The game he developed was too hard! If you entered the code, referred to as the Konomi Code, you would receive the full amount of power-ups usually attained throughout the game!

So, the code has permeated pop culture throughout the years. It appears in various forms in Netflix, Google Hangouts, Wreck-it Ralph, The Incredibles, Archer, Fortnite and even the M&S Christmas website would drop down funny characters. For now, just say, “up up down down left right left right B A Start” to Siri and see what she says!!

So, I prefer to think of Physics as the Konomi Code to the universe. We have the cheat codes and hopefully, by the end of the class, you will see the world just a little bit differently!!

The same thing can be said for Michael Jordan’s foul line dunk! How long do you think he was in the air?

You may ask, “Why the heck is there a bee in the blog?” And the answer may surprise you but hopefully it dazzles you as well!

Remember we mentioned the term vector earlier when describing velocity? This means velocity has a magnitude AND direction. Speed can be considered the magnitude of velocity with any directional descriptor (up, down, left, right, east or west) serving to describe the direction. Well, it turns out that position and displacement are also vectors. So if I walk to the movie theater, I can that I traveled 33 meters north to the cinema.

It turns out that the same type of lingo can be used to describe the displacement of a bee during pollination of a bunch of flowers. If a bee zig zags across a small field sipping on nectar, he uses this concept of vectors to find his way home to the hive.

Does the bee have to revisit each of the flowers it pollinated to find his way home?

There is nothing more soothing than a bluebird day, especially in the fall where that high pressure lowers the humidity and gives us incredibly beautiful blue sky! But why? Why is the sky blue? Why are clouds white? Why are sunsets red? We have some beautiful sunsets over Lake Champlain that fill up our Instagram feeds with various hashtags. Light coming from the sun is made up of all the colors of the spectrum each of a different wavelength and appears to the human eye as white light. Ever stare at the sun, well don’t, but if you did, you would see pretty much white. Visible light appears white because it is a combination of all colors. In the visible spectrum, discovered by Isaac Newton, violet and blue are of short wavelengths and red and orange lace larger wavelengths. Remember ROY-G-BIV?

Now, the atmosphere is made up of all sorts of molecules, dust, smoke and all other things we pollute it with. But mostly nitrogen and oxygen. As sunlight passes through the atmosphere, it strikes these very small molecules in which shorter wavelengths are absorbed and then kicked out in a pattern called Rayleigh scattering. Largest wavelengths continue to pass through with out being scattered and, voila, blue sky!! You can think of them as optical tuning forks!

During sunset, the light from the sun has to travel much farther through the atmosphere to reach the earth due to the geometry of its position. This allows for plenty of time for the blue light to be scattered all over and the red light to pass on through to your eye because of your current angle to the sun!!

Pink sky at night Shepherd’s delight? Well, kinda? Weather travels from West to East. Really good sunsets occur with high pressure squash all the molecules down to the surface so more and more blue light is scattered so red really pops!! So a really good sunset in the western sky is going to travel eastward for the morning in the East. The high pressure will be here in Vermont and high pressure means beautiful sunny day!

Does it rain more often on the weekends or is that an Old Wives Tale? It’s true!! It’s 22% more likely to rain on Saturday than Monday on the East coast of the US. As humans, we produce more pollution during the work week that act as microscopic starters for rain droplets!! Therefore, Monday through Wednesday are bright and sunny and then it’s buckets on the weekend!! Check out this video!!

Here are a couple video resources that will help you in understanding!!!

Crash Course

Bozeman Science

Isaac Newton

On Christmas Day 1642, the year Galileo died, Isaac Newton was born in his mother’s farmhouse prematurely and barely survived. He was not particularly exceptional and dropped out of school to work on the family farm, which he hated as he preferred books given to him by his pharmacist neighbor. Isaac’s uncle sensed a spark and prompted him to study at Cambridge where he graduated with no particular distinction.

In 1665, a great plague swept through England forcing a 23 year old Isaac to continue his studies at home. It is here where he laid the foundations for physics extending from Earth to the Heavens. He developed Universal Gravitation, Calculus and his iconic Laws of Motion as well as explored the nature of light.

He is somewhat of a superhero and on his grave in Westminster Abbey, it reads, “Mortals rejoice that there has existed such and so great an ornament of the human race.”

In honor of the great thinker, I have developed a Newton of Fig Newtons lab!!!

We will be doing the amazing Speed of Sound lab soon!

I remember so vividly when my high school physics teacher, Mitch Johnson, said, “Cartoons are funny because they defy the laws of Physics.” He said it so matter-of-factly that I only wrote an entire essay about it on my application to Oxford! The Simpsons, in all its genius, echo the notion with the couch gag depicted above. Why is it funny?

Now check out this amazing world record setting trampoline video!! The amount of our year contained in this video is astonishing!! While you’re here, this basketball dribbling video is just about everything!

I happen to love hummingbirds!! They have beautiful iridescent throats that dazzle the eye. They are acrobats with a mind-bending figure 8 wing flap allowing for lift on both the up and down strokes lending to their characteristic float. They are designed for quick elusive movements due their relatively small moment of inertia around the roll axis. They are very similar to the snitch in Harry Potter in this regard!! They are essentially Physics machines! So, in order to truly understand the hummingbird, or any other loving organism, or the world around us or even the physical universe, we need to understand Physics and it’s principles!

What is Physics??

If you look up the definition of Physics, you’ll probably find something to the likes of “the science of matter and energy and the interactions of the two”. I’m sorry, I missed that as I just fell asleep!

I prefer to think of it as the Konomi Code to the Universe!!

Back in 1985 Kazuhisa Hashimoto was working on the arcade game Gradius. During testing, he found the game incredibly challenging so he developed a shortcut that allowed him to easily get to where he needed to be without dying. The code, referred to as the Konomi Code, gives the player a full set of power-ups usually afforded throughout the game!

If you enter “up up down down left right left right B A Start” you will attain the necessary power-ups; most notably you will receive 30 lives in the classic NES game Contra.

Now, this code has permeated throughout pop culture with appearances in Wreck-it Ralph, Bank of Canada, Archer, Gravity Falls, Fortnite, The Incredibles, the 2016 Marks and Spencer Christmas site in England, Google Hangouts and various Conde Naste UK sites. However, you can just grab your iPhone and say the code to Siri!!!

In Physics, we manipulate the Konomi Code to the universe. We have the cheat codes. So, hopefully, by the end of the class you will you will look at the world just a bit differently. In particular, this video of Flanders and how it relates to the padding underneath the backboards in the gym!! Why is it so funny!?!

Let’s see what I mean in the next couple of examples!

The 2020 British Grand Prix looked like it was going to be smooth sailing for the great Lewis Hamilton. Throughout a brilliant race, Hamilton had built a lead of over 30 seconds. Well, you no what they say, you can never count your chickens before they’re hatched! What happened next was truly one of the most exciting finishes in all of sport!! Check out the race recap narrated by the best there is, David Croft and Martin Brundle!

We want to know if/when and where Max Verstappen catches up to Lewis!! Let’s delve! And you can’t find out the results here!!

Well, that was super fun!! Now let’s analyze the trend that’s sweeping the nation…Maria Kart in a laundry basket on a treadmill into a pool!!

Linearization!!

Here is our first topic!! It involves a process of linearization which is an important and powerful tool for data analysis and the development of relationships!!

Here is the Jumping Jumper Elves lab to practice linearization!

I would absolutely recommend watching this video concerning graphs of position/velocity/acceleration as a function of time

Below you will find links to YouTube channels that are very useful to the course!!

Flipping Physics

Matt Anderson

AP Daily