Notes: Describing MotionLevel 1: Scalars vs. VectorsObjectivesBy the time you finish this level, you need to be able to:

a. Define kinematicsb. Describe the difference between one and two dimensional kinematicsc. Define scalar and vector.d. Organize values into scalars and vector.e. Give an example of a scalar and a vector.

Introduction to KinematicsThe first two sections of physics deal with describing the way object move, which is called kinematics. We will first look at kinematics in one dimension, which describes the motion of object moving back and forth (see the picture below on the left). Later, we will look at more complicated situations in kinematics in two dimensions, which describes motion moving up and left, down and right, back and up (see the picture below on the right)…Later on in the year, we will explore why objects

move.

We will be describing these motions both in words and in mathematics. Don’t be intimidated by the math. I know just me writing those words sends shivers of terror down some of your spines. Nearly all the math we deal with in this class will involve pretty easy algebra and trig. Many people who do not like math by itself still end up loving physics.

Vectors and ScalarsBefore we start, we need to distinguish between two key ideas: vectors and scalars. Vectors have a magnitude and a direction, while scalars only have a magnitude. That sentence probably made no sense to you, so let me show you an example.Scalar Magnitude

45 mi65 km4.3 x 108 cm2 m33 mph

Vector Magnitude Direction 45 mi North65 km East4.3 x 108 cm down2 m in the positive direction33 mph South

In everyday life, directions rarely matter, unless we are using GPS. In physics, they matter a great deal. We often need to use them to keep track of where objects are moving in our problem.Vectors as Positives and NegativesSometimes, when we are describing a vector, we will use north, south, up, down. In some longer problems, this gets confusing and time consuming. To save us time (and stress), we can use a math trick. We can choose one of the direction as positive and one of the direction as negative. We won’t go into too much detail here (it’s better just to learn it as we go), but for now, just know that vectors can also look like this: +22 mi, -4.7 x 102 m…The positives and the negatives show us the direction. This will make more sense in the next section.

Level 2: Distance vs. DisplacementObjectivesBy the time you finish this section, you need to be able to:

a. Define position, distance and displacement.b. Differentiate between distance and displacement.c. Calculate distance and displacement.d. Show what a negative displacement would look like.e. When given a scenario, determine an object’s distance and displacement.

Describing Motion in WordsIn physics, we use very precise language when describing motion. It is important for you to learn all the terms below. Read the different sections, and then I will summarize them for you at the end of the unit.

PositionPosition is where the object is at. We use the symbol x for this. In the situation below, the car’s position is at +2 m.x=+2 m.

DistanceDistance is how far an object travels.Let’ have our car move. Let’s have it drive 3 meters, from x1=2 to x2=-1 m..

We often use distance in everyday language, and it’s just what you think it is. If I asked you for the distance the car moved, you would say it moved 3 meters. Easy-peazy. Notice that we didn’t talk about the direction- that means distance is a scalar. When we talk about distance, we don’t care whether the car moved forward or back, just that it moved 3 meters.DisplacementMore often than not, we don’t use distance in physics- we use displacement, which tells us the magnitude and direction of a change in position. Let’s look at the car moving again, from x1=2 to x2=-1 m.

With displacement, we don’t just car that the car moved 3 meters, we also care that the car moved in the negative direction. It tells us precisely where the car is now. If we don’t state the direction, when we say “the car moved 3 meters” it could mean that the car moved backward to -1 m or the car moved forward to 5 m. We just don’t know. Displacement clears that up. When we state the displacement of an object, we are stating how far it moved and the direction it moved in.

displacement=x f−x iIn other words, the displacement equals the final position minus the initial position.

The car’s initial position was 2 m, so we would say: x i=2

The car’s final position was at -1 m, so we would say: x f=−1

x i=2 x f=−1

displacement=x f−x idisplacement=−1−2

displacement=−3m

In other words, the total displacement was 3 meters in the negative direction, or -3 m.Remember that the distance was 3 m, while the displacement was -3 m. Don’t think that displacement is just a negative version of distance. It’s not! In the next example problem, we will help clear that up.There is an easy way to tell the difference between distance and displacement. You can think of distance as the total distance you traveled, while displacement is how far you are from where you started. The picture on the right helps illustrate this.

Let’s take a look at an example to help make this idea clear.

Example Problem: Kanye DancesKanye West is dancing. He starts out at +4 m. He then shimmies over to +10 m. Then he does a moon walk all the way over to -7m.

1. What is the total distance Kanye danced?2. What is Kanye’s displacement?

Solution1. Kanye traveled 6 m forward. He then moved 17 m back. Distance= 6+17= 23 m.2. Kanye has moved -11 m from where he started. The negative sign tells us he

moved in the negative direction.

Level 3: Speed vs. VelocityObjectivesBy the time you finish this section, you need to be able to:

a. Define speed and velocity.b. Differentiate between speed and velocity.c. Calculate speed and velocity.d. When given a scenario, determine an object’s distance, displacement, speed and

velocity.In the last section, we talked about describing where an object is and how far it has moved. Now we are going to discuss how fast objects go.SpeedYou are already familiar with speed. You use speed all the time when you talk about how fast your car is racing along. Speed tells us how fast an object moves through a distance. It does not care about direction. It does not care if you went 70 mph forward and then 70 mph backward. Speed is a scalar, so only the magnitude (the amount) matters.The equation for speed is pretty easy:

speed=distancetime

Look at the equation for speed. Distance (in the numerator) is measured in meters (our standard units) and time is measured in seconds. Therefore, the standard units for speed are m/s. Speed is not used very often in physics. Because of this, it doesn’t have an official symbol- you can just use s or write “speed”.Example ProblemOn your way to class, you walk a total distance of 57 m.

a. If it takes you 75 seconds to get to class, what was your speed?b. If it takes you 2 minutes to get to class, what was your speed? Your answer

should be in m/s. (Convert! Convert!)There are two different types of speed. Instantaneous speed is how fast an object is moving in the moment. For example, a speedometer tells you the instantaneous speed of your car- how fast it is moving at that exact second.

Average speed tells you how fast the object was moving on average (duh). In other words if you went 60 miles in one hour, you were moving on average 60 mph. That does not mean that every single second of the trip you were going 60 mph. Maybe you were only going 40 mph for one portion and 80 mph in another. Maybe you were stopped for awhile to get a delicious Mocha Cookie Crumble Frappuccino. Overall, however, on average, you were going 60 mph. We have an equation for this:

average speed= totaldistancetime

VelocityVelocity is used constantly in physics- it appears in every major section of physics. Velocity is similar to speed-it’s another way of describing how fast something is moving- except that we care about the direction. Because of this, velocity is based on displacement.

velocity=displacementtime

v=dt

Velocity is also measured in m/s, and the symbol we use to represent it is v.Practice Problem: Speed vs. VelocityA car starts out at -5 m, drives forward to +6 m, and then backward to -1 m. It does this maneuver in 8 seconds. Find the car’s a) average speed b) velocity

Solutiona. To find speed, we remember that:

speed=distancet

What distance did the car travel? Distance is the total journey of the car. In this case, that is 7 m forward and then 11 meters back. All together, that’s 18 m. This took 8 seconds, so we can write:

distance=17mt=8 s

speed=distancet

Figure 1: This is worth stopping for.

v=188

v=¿2.25 m/s

b. If we want to find the velocity, we need to know the displacement. Displacement is how far the object is away from where it started. That means the car is -4 m away from where it started. Notice I needed to include the negative sign. This is because the car has moved backward (in the negative direction).

displacment=−4mtime=8 s

v=displacementtime

=dt

v=−48

v=−0.5m /s

Notice that the velocity can be negative- it means that the car moved in the negative direction. It does not mean the car is moving slowly.

Level 4: AccelerationObjectivesBy the time you finish this section, you should be able to:

a. Define acceleration.b. Differentiate between “acceleration” in everyday language and “acceleration” in

scientific language.c. Describe three ways an object can accelerate.d. Read a scenario and evaluate whether the object involved is accelerating or not.e. Describe uniform and non-uniform acceleration.f. Calculate acceleration in a wide range of scenarios.

In everyday language, when we say something is accelerating, we mean it is speeding up. In physics, acceleration has a more broad definition. Acceleration means a change in velocity.Key IdeaAcceleration is a change in velocity.Remember that velocity has specific parts. It always includes both a magnitude and a direction.

45 m/s NorthMagnitude

Direction

Acceleration occurs when we change any of these parts. That means that an object is accelerating if it is speeding up (changing magnitude), slowing down (changing magnitude) or changing direction.Key IdeaAn object is accelerating if it is speeding up, slowing down, or changing direction.

This takes a while to get used to. Even AP Physics students sometimes get confused- sometimes I even slip up and say the wrong thing. For some students, this immediately makes complete sense. For others, it takes a lot of practice.Example Problem: Accelerating?Circle the objects that are accelerating.

a. A blimp is moving steadily across the sky.b. A speeding car, going 60 mph) whips around a bend in the road.c. A horse races across a field at an extremely fast pace.d. A delivery truck slows down at a stop light.

e. A rocket starts off at rest on the launch pad, but speeds up as it rises.f. A puppy slows to a stop as it slides across a tile floor.

One trick- you can tell if an object is NOT accelerating because it is doing one of two things: sitting still, or moving at a constant velocity in one constant direction. If it is not doing one of these things, it is accelerating.

Uniform and Non-uniform accelerationObjects can speed up, slow down and change direction in lots of ways. Uniform acceleration means the object is changing its velocity at a steady rate. Maybe it is getting faster and faster at a steady pace. Maybe it is slowing down in a predictable steady manner. We also call this type of motion constant acceleration. If the object speeds up quickly, then speeds up more slowly, it isn’t moving in a nice, steady predictable way. We call this type of motion non-uniform acceleration or non-constant acceleration. Compare the two motions below to make sure you understand this.

Calculating AccelerationAcceleration, as we said, is a change in velocity over time. In other words:

acceleration= change∈velocitytime

= final velocity−initial velocitytime

=v f−v it

or, put more simply,

a=v f−vit

The units for velocity (in the numerator) are m/s . The units for time are s. So, the units for acceleration are m/s/s. We can also write this as m/s2.

Example ProblemA dog is chasing after a stick. He starts off walking with a velocity of 2 m/s. Ten seconds later, he is going 9 m/s. What is the dog’s acceleration? Don’t forget to follow all the problem solving steps.

vi= 2 m/svf= 9 m/sa=?t= 10 s

a=v f−vit

a=9−210

a= 710

a=0.7 ms2

Sometimes problems don’t come out and explicitly tell us exactly what we are looking for. The information can be hidden in the story of the problem. For example, if an object starts at rest, this means vi =0 m/s. If the object comes to a stop, this means vf=0 m/s. The following example problems lets you try this out. Example ProblemA car is slowing down at a stop light, experiencing an acceleration of -2.3 m/s/s. It takes 30 seconds for the car to come to a complete stop. What was the car’s initial velocity?vi= ?vf= 0 m/s (it is coming to a stop)a=-2.3 m/s/st= 30 s

a=v f−vit

−2.3=0−vi30

(−2.3 ) (30 )=0−v i

−69=−v i69m /s=v i

Some of the math above may have been tricky for you. Don’t just stare at the problem- you will need to solve problems like this when you take your challenge in a little while. Ask your group members for help. If all of you are struggling, keep looking at it. I will be around soon to help you. If you are really stuck, put a question mark by this problem, and move on. Do not just hang out waiting for me.