Kinematics Physical Science Unit 1 Notes, examples, and graphics adapted from Physicsclassroom.com

Expectations No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking No one leaves during notes Be prepared to participate

Describing motion Scalars, Vectors, Distance and Displacement

Questions What is mechanics? What is kinematics? What is a scalar? What is a vector? How are distance and displacement different? Draw a vector that is 3 inches long to the left. Give an example of a vector and a scalar. Give a real world example of someone traveling a large distance with a zero displacement

One of the topics in a physical science class is motion. Mechanics is the study of the motion of objects. Mechanics is studied using kinematics, or the science of describing motion using: Words Diagrams Numbers Graphs equations

Language of kinematics What are some words that describe motion? We will add to the list we create. We will use math to describe motion as well.

Scalar vs. Vector Sort these words into two groups. Distance acceleration force Weight volume time Mass displacement density Velocity speed

Mathematical quantities are either vectors or scalars. Scalars: quantities that are describe by numbers alone Vectors: quantities that are described by numbers and a direction https://youtu.be/A05n32Bl0aY

Check Your Understanding Quantity Category a. 5 m55 See Answer b. 30 m/sec, East c. 5 mi., North d. 20 degrees Celsius e. 256 bytes f. 4000 Calories

Answers Quantity Category a. 5 m See Answer: Scalar b. 30 m/sec, East See Answer: Vector c. 5 mi., North d. 20 degrees Celsius e. 256 bytes f. 4000 Calories

Distance & Displacement Distance is scalar, and only refers to how far an object has traveled. Displacement is a vector quantity and refers to how far an object has moved from its original place.

Consider the motion shown below: I walked 4m East, 2m South, 4m West, and 2m North. What is my distance? What is my displacement?

Another example Find the displacement and distance for the skier during the three minutes they moved from A to B to C to D.

How do I solve for the distance? How do I solve for the displacement? What is the distance? What is the displacement?

Consider a football coach pacing the sidelines. What is their displacement at B, C, & D? What distance have they traveled at each?

Practice What is the displacement of the cross-country team if they begin at the school, run 10 miles, and finish back at the school? What is the distance and the displacement of the race car drivers at the Indy 500?

Questions What is mechanics? What is kinematics? What is a scalar? What is a vector? How are distance and displacement different? Draw a vector that is 3 inches long to the left. Give an example of a vector and a scalar. Give a real world example of someone traveling a large distance with a zero displacement

Expectations No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking No one leaves during notes Be prepared to participate

Describing Motion Speed (Instantaneous vs Average) and Velocity

Questions How is speed different from velocity? How are speed and velocity similar? How is instantaneous speed different from average speed? What is the equation to calculate average speed? What is the equation to calculate velocity?

Speed & Velocity Speed is a scalar quantity that refers to how fast something is moving compared to another object. Velocity is a vector quantity that refers to how fast an object changes its position. When solving for velocity you must include a direction!

The direction of a velocity vector is the same as the direction the object is moving. In great detail describe your trip to school today from leaving your driveway to arriving at the school doors.

In your description of traveling to school, if you came by car, did you travel the same speed the entire time? Why or why not? How do you know?

Instantaneous speed: the speed at any given instant; the speed “right now.” Average speed: the average of all instantaneous speeds; found by calculating: distance time

Average Speed Distance Speed Time

Velocity Displacement Velocity Time

Solving problems using the triangle equations. https://youtu.be/rjjmHoVktuc

Practice While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed? Remember the rectangular walk from last time? If that walk was completed in 24 seconds, what is the average velocity?

Questions How is speed different from velocity? How are speed and velocity similar? How is instantaneous speed different from average speed? What is the equation to calculate average speed? What is the equation to calculate velocity?

Expectations No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking No one leaves during notes Be prepared to participate

Describing Motion Acceleration

Questions What is acceleration? Is acceleration vector or scalar? How is acceleration calculated? How is acceleration labeled, and why? Explain the difference between constant acceleration and changing acceleration. Explain the difference between constant acceleration and constant velocity.

Acceleration Acceleration is a vector quantity that describes how fast something is changing its velocity. Acceleration can mean: Speeding up Slowing down Changing direction Since it is a change in velocity over time.

Constant acceleration means that the velocity is changing by the same amount over a standard unit of time. What is the acceleration of this object to the right?

Changing acceleration means that the change in velocity is not showing a constant pattern as time goes on.

Calculating Acceleration The average acceleration of an object can be found by using the following equation: The triangle in the equation is a delta, and means, “change in”. So, you would subtract your initial velocity from your final velocity and divide by the time.

Acceleration Time Final Velocity – initial velocity Average acceleration Time

Acceleration values (labels) are given in velocity/time. There will ALWAYS be two units of time if something is measuring acceleration. Velocity is already measured with a unit of time and now we are adding in how fast the velocity is changing, hence, two units of time.

Examples of units of acceleration: m/s/s or m/s2 Mi/hr/s Km/hr/s Cm/m/s

Acceleration vectors Since acceleration is a vector, it has direction. The direction is dependent on: Is the object slowing down or speeding up? Is the object moving in a + or – direction?

The general idea is that if the object is slowing down, then the acceleration is in the opposite direction of the motion.

Positive acceleration Why is example B +acceleration?

Negative acceleration

The positives and negatives of acceleration and velocity are important because they give us information about the direction of the object when we don’t have the word to describe the direction.

Check Your Understanding Find the acceleration for the following two data sets.

Questions What is acceleration? Is acceleration vector or scalar? How is acceleration calculated? How is acceleration labeled, and why? Explain the difference between constant acceleration and changing acceleration. Explain the difference between constant acceleration and constant velocity.

Expectations No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking No one leaves during notes Be prepared to participate

Describing Motion Introduction to diagramming motion

Sometimes is it easier to understand motion when looking at a “picture” of the motion. Ticker tape (dot) diagrams can be used or Vector diagrams work well, too.

Ticker tapes are papers pulled through a machine that records whether the paper is moving at a constant rate or accelerating and whether it is moving quickly or slowly.

Vector diagrams show the motion and magnitude with arrows.

When an object is maintaining velocity the arrows have the same magnitude; when it is accelerating, they do not.

Check Your Understanding Sometimes, ticker tape diagrams are called oil drop diagrams because they show the motion as if your car were leaking oil. Renatta Oyle owns such a car and it leaves a signature of Renatta's motion wherever she goes. Analyze the three traces of Renatta's ventures as shown below. Assume Renatta is traveling from left to right. Describe Renatta's motion characteristics during each section of the diagram. 

Questions What is acceleration? Is acceleration vector or scalar? How is acceleration calculated? How is acceleration labeled, and why? Explain the difference between constant acceleration and changing acceleration. Explain the difference between constant acceleration and constant velocity.

Expectations No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking No one leaves during notes Be prepared to participate

Describing Motion Position v. Time Graphs

Questions What does the position tell you about an object on a position-time graph? What does it mean if the position-time graph has negative y-axis values? What does it mean if the slope is negative on a position-time graph? What does an object at rest look like on a position-time graph?

The shape and the slope of the lines on a position-time graph tell you specific things about the movement of an object. Due to the appearance of the graph you can determine the velocity, acceleration, and distance traveled in an amount of time.

Consider a car moving constantly at 10m/s to the right

A constant, positive velocity results in a constant, positive slope. But what if the velocity is not constant, and is instead shows acceleration?

If the velocity is not constant, then the slope will not be constant.

Two types of motion - slope Constant velocity Changing velocity

The importance of slope As the slope goes, so goes the velocity. If the slope is constant, so is the velocity If the slope is changing, so is the velocity If the velocity is negative, so is the slope If the velocity is positive, so is the slope The steeper the slope, the faster the object is moving. A gentle slope = slower velocity

Slower v. faster slope

Which is traveling faster? What direction are they traveling? How do you know?

Accelerated Motion Curved lines have a changing slope which means that something is accelerating. This could apply to any slope, positive or negative.

Below, we have two graphs with negative velocity and changing slopes. One changes from slow to fast, and the other from fast to slow. Which is which?

Fast-slow Slow-fast

Check Your Understanding Describe the motion of the objects depicted by the two plots on the next slide. In your description, be sure to include such information as the direction of the velocity vector (i.e., positive or negative), whether there is a constant velocity or an acceleration, and whether the object is moving slow, fast, from slow to fast or from fast to slow.

Check Your Understanding

Meaning of slope The actual value of the slope on a position-time graph tells you the velocity of an object. Slope can be described as: Straight Curved Steep Gentle + more

Consider the two examples below What do you notice about the two graphs? How are they the same? How are they different? How far does the car travel in graph #1 compared to #2?

Determining Slope Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Let’s try to figure the slope Answer on next slide 

Let’s try to figure the slope Using the two given data points, the rise can be calculated as -24.0 m (the - sign indicates a drop). The run can be calculated as 8.0 seconds. Thus, the slope is -3.0 m/s.

Check Your Understanding Determine the velocity from the graph below.

Questions What does the position tell you about an object on a position-time graph? What does it mean if the position-time graph has negative y-axis values? What does it mean if the slope is negative on a position-time graph? What does an object at rest look like on a position-time graph?

Expectations No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking No one leaves during notes Be prepared to participate

Describing Motion Velocity v. Time Graphs

Questions What does the slope tell you on a velocity-time graph? What does a negative slope mean on a velocity-time graph? What does the area under a velocity-time graph line show you? Compare and contrast position-time graphs and velocity-time graphs.

Velocity-time graphs and position-time graphs can look very similar. The only thing that is different is the y-axis. You must pay close attention to the label to know which graph you are looking at. They can give very different information!

Constant v. changing velocity If a car is moving to the right at 10m/s with a constant velocity, it has zero acceleration. A graph for such motion would look like a position-time graph where the object was sitting still, BUT it instead has a constant velocity, or zero acceleration.

So, when we plot an object that has a constant velocity on a v-t graph, we have zero slope. If we have a changing velocity, then the line has a slope of some value.

Remember the slope on a p-t graph gave us information about velocity? The slope on a v-t graph gives us information about the acceleration of an object. Zero slope = zero acceleration

Because the slope on a v-t graph gives information about acceleration, we need to know how to recognize positive and negative acceleration. This is where reading a graph is very important.

Know your graph regions! If the object is in the positive section of the graph it is moving in the positive direction. If the object is in the negative section of the graph it is moving in the negative direction If the object crosses from the positive to the negative region of the graph, then the object has changed directions.

Speeding up? Slowing down? Look at where the line is going! The closer it gets to zero then it is slowing down!

Check Your Understanding Describe the motion of the object in the graph: + or – direction? Constant velocity? + or – velocity? Slowing or speeding up? Direction? + acceleration or?

Looking at slope Slope on a v-t graph is your acceleration Zero = no slope + = a positive slope - = negative slope Steep line = high acceleration Gentle line = low acceleration All of this is calculated the same as any slope. Rise over run.

A few examples Time Velocity 0 10 1 10 2 10 3 10 4 10 5 10

Time Velocity 0 0 1 10 2 20 3 30 4 40 5 50

2-Stage motion Time Velocity 0 2 1 2 2 2 3 2 4 2 5 4 6 6 7 8 8 10

Check Your Understanding The graph for a 2-stage rocket is shown below. Determine the acceleration during the three time intervals, and describe the motion in words.

Shape and Motion Relating the shape to the motion of an object can help you understand what is going on with the object. We will look a few examples.

Check Your Understanding Describe the motion of the following 3 objects in the graphs.

Determine the slope We determine the slope exactly as we did for the p-t graph. Determine the acceleration for the following graph.

Determining Area One other piece of information that a v-t graph can provide is the displacement of the object. This is done by calculating the area that falls between the line and the axes. 3 examples:

We use the formulas for finding the areas of triangles and rectangles to find the area under our lines. Let’s practice!

Questions What does the slope tell you on a velocity-time graph? What does a negative slope mean on a velocity-time graph? What does the area under a velocity-time graph line show you? Compare and contrast position-time graphs and velocity-time graphs.

Expectations No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking No one leaves during notes Be prepared to participate

Free Fall

Questions What is free fall? What acceleration does an object in free fall show? Compare the speed and distance of an object in free fall at one second intervals for 6 seconds.

Free Fall A free falling object is an object that is falling due to the force of gravity. Any object that is acted upon ONLY by gravity is said to be in free fall. Free falling objects: DO NOT encounter air resistance Accelerate at 10m/s/s (9.8m/s/s or 32 ft/s/s)

A dot diagram is a great way to show an object that is in free fall, like that to the right. The distance increases each second, which is a sure sign that the object is accelerating as it falls.

The acceleration of gravity is represented by the letter g It is equal to 9.8m/s/s on Earth, but we will use 10m/s/s for ease of computations. g will be different at different locations in the solar system due to different gravitational forces.

How Fast? How fast an object is free falling depends on how long it has been falling. The equation v=tg will give us the approximate velocity for an object in free fall. V= velocity t=time g=acceleration of gravity

Acceleration of gravity Time (s) Acceleration of gravity velocity 1 10 2 20 3 30 4 40 5 50 6 60 7 70 8 80 9 90

How Far? How far an object in free fall has traveled depends on the amount of time it has been falling. Because it travels farther each second due the acceleration, we have an equation to help us calculate the distances that are involved. How far= ½ gt2 g= acceleration of gravity t=time

Acceleration of gravity Time Acceleration of gravity Distance traveled 1 10 5 2 20 3 45 4 80 125 6 180 7 245 8 320 9 405

Questions What is free fall? What acceleration does an object in free fall show? Compare the speed and distance of an object in free fall at one second intervals for 6 seconds.

End of unit one