1. Linear Motion Physics

2. Linear Motion Linear Motion refers to “motion in a line”. The motion of an object can be described using a number of different quantities. Time – How long an object is in motion for. In physics, we usually use seconds but in every day life we use minutes, hours, years, etc. Distance – how far something travels along its path. Can be measured in a wide variety of measurements including kilometers, meters, inches, feet, etc.

3. Let’s do a Frayer model for linear motion: Definition: How to remember: Drawing: Motion in a straight line linear motion verticalhorizontal What it’s NOT:

4. Speed, velocity, acceleration Speed - How fast you’re going 15 km/hr, 22 cm/s, 2000 mi/hr Velocity – how fast you’re going in a certain direction Acceleration - how fast your velocity is changing (speeding up or slowing down) Example word problem: A soccer ball is moving horizontally at a speed of 3.0 m/s. It then undergoes a constant negative acceleration. After 4.0 s, the ball is moving at 1.5 m/s.

5. ● Instantaneous Speed is the speed at any specific instance or moment in time o Ex. On a speedometer reading… you are traveling 35 mph (mi/hr) or 50 km/h or 25 m/s ● Average Speed is the total distance covered divided by total time Types of Speed

6. How do you calculate average speed? ● The average speed of an object is defined as the total distance traveled divided by the total time elapsed Average Speed = total distance total time Speed = d t Michael Phelps can swim a 200 m butterfly race in 1:52.09. What would be his average speed?

7. Speed, cont Speed is a scalar quantity, meaning it has no direction. Other examples include distance and time. Example: speed: I was going 75 mi/hr mass: I weigh 75 kilograms time: there are 45 minutes left of class

8. Vector Some quantities are vectors, meaning a number with a unit and direction Common vectors that we deal with in physics include displacement, velocity, and acceleration.

9. Pictorial Representation ● An arrow represents a vector o Length = magnitude (size) of vector o Direction = direction of vector

10. Pictorial Representation ● This arrow could represent a vector of magnitude 10 point to the “right” ● This arrow could represent a vector of magnitude 5 point to the “left”

11. Practice! ● Draw an empty Venn Diagram like this Scalar Vector

12. Label one side scalar, other vector ● Magnitude ● Size ● Direction ● Units ● Distance ● Displacement ● Speed ● velocity ● Acceleration ● Mass ● Weight ● 12 cm ● 47 kg (mass) ● 470 Newtons (weight) ● 50 meters ● 50 meters West ● 25 m/s ● 25 m/s toward home ● 25 m/s away from home ● 10 m/s 2 ● 10 m/s 2 toward the ground Place these words in the correct space on the diagram:

13. Displacement vs. distance: 1. Displacement: how far its position is from the starting point (in meters with a direction). A measurement of how far you “displaced” meaning changed your position. Remember, displacement is a vector so you need a direction! Example: I can jump 4 feet, up. o Distance: how far an object travels (in meters)

14. Displacement Isn’t Distance ● The displacement of an object is not the same as the distance it travels o Example: Throw a ball straight up and then catch it at the same point you released it  The distance is twice the height  The displacement is zero

15. Distance & Displacement

16. B A C 5 m 4 m 3 m Your distance traveled is 7m You walk from A to B to C. What is your distance traveled? What is your displacement from A? Your displacement form A is 5 m

17. Horizontal Displacement When displacement is horizontally oriented, we refer to an “imaginary line”. Any displacement to the right (or forward) of the line, we have a positive displacement. Any displacement to the left (backwards) of the line, we experience a negative displacement.

18. Vertical Displacement Just as we do with horizontal displacement, we refer to an imaginary y-axis. Moving up the line will be a positive displacement, and moving down the line will be a negative displacement.

19. Let’s do Frayers for distance & displacement: Definition: Don’t confuse this with:How to remember: Drawing:

20. Velocity ● The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed ● Velocity is a vector quantity Average Velocity = total displacement total time V = x t

21. Velocity ● It takes time for an object to undergo a displacement ● The average velocity is rate at which the displacement occurs ● generally use a time interval, so let t i = 0 V (average) = Δx = X final – X initiative = x f - x i Δt t final – t initiative t

22. Velocity, cont. ● Pull back car example and demonstration

23. Speed vs. Velocity ● Cars on both paths have the same average velocity since they had the same displacement in the same time interval ● The car on the blue path will have a greater average speed since the distance it traveled is larger

24. Let’s do Frayers for speed & velocity Definition: Don’t confuse this with:How to remember: How to calculate:

25. Speed vs. Velocity ● You drive from Yakima to Seattle (140 miles away) ● You stop in Ellensburg for a 2 hr lunch with a friend. ● Your total driving time is 2 hours ● What is the average speed? ● What is the average velocity? ● Remember, speed = total distance/ total time

26. Concept Map: Linear Motion The position changing How quickly the position changes called which is calculated by Adding all legs of the journey distance displacement speed velocity X final –x initial Total distance Total time x final –x initial time

27. Acceleration ● Acceleration is a measure of how quickly velocity is changing. ● Change in velocity divided by the change in time TIME0.00 sec1.00 sec2.00 sec3.00 sec4.00 sec VELOCITY0 mi/hr10 mi/hr20 mi/hr30 mi/hi40 mi/hr

28. Acceleration Great animation showing acceleration: http://www.physicsclassroom.com/mmedia/kinema/acceln. cfm ● Changing velocity (not constant) means an acceleration is present ● Units: m/s 2 (SI) other examples: cm/s 2 ft/s 2

29. Relationship Between Velocity & Acceleration ● Uniform velocity (shown by red arrows maintaining the same size) ● Acceleration equals zero

30. Relationship Between Velocity & Acceleration ● Velocity and acceleration are in the same direction ● Acceleration is uniform (blue arrows maintain the same length) ● Velocity is increasing (red arrows are getting longer) ● Positive velocity and positive acceleration

31. Relationship Between Velocity & Acceleration ● Acceleration and velocity are in opposite directions ● Acceleration is uniform (blue arrows maintain the same length) ● Velocity is decreasing (red arrows are getting shorter) ● Velocity is positive and acceleration is negative

32. Acceleration Sometimes we are given acceleration and want to know the velocity of an object after a certain amount of time passes. We can figure the velocity out by simply rearranging the equation: To look more like: Velocity final = Velocity initial + at

33. Let’s do a Frayer for acceleration : Definition: Don’t confuse this with:How to remember: How to calculate:

34. Acceleration Example 1 A bird is flying at a speed of 35.8 m/s. If it takes 2.0 s to come to a complete stop, what acceleration would it have?

35. Example 2 I can run at a speed of 25 m/s and accelerate at 3.0 m/s/s for 5 seconds. How fast would I be running after 5 seconds?

36. Acceleration Example 3 ● A car is said to go "zero to sixty in six point seven seconds". What is its acceleration in m/s 2 ?

37. Acceleration example 4 A toy traveling at 50 cm/s and slows down to 20 cm/s in 10 seconds. What is the toy’s acceleration?

38. Concept Map: Linear Motion The position changing How quickly the position changes The rate at which the movement changes called which is calculated by Adding all legs of the journey distance displacement speed velocity acceleration X final –x initial Total distance Total time x final –x initial time v final –v initial time called