1. Unit 3: One Dimensional Kinematics

2. Section A: Velocity and Acceleration Corresponding Book Sections: Corresponding Book Sections: –2.2, 2.4 PA Assessment Anchors: PA Assessment Anchors: –S11.C.3

3. What is kinematics? Kinematics Kinematics –The study of motion and how to describe it –Does not consider what causes the motion One Dimensional (1D) Kinematics One Dimensional (1D) Kinematics –Motion in a straight line  Left/right, up/down, east/west, etc

4. Coordinate system Defines position of an object Defines position of an object xfxf xixi x = 0 + Indicates the positive direction

5. Basics of a coordinate system Establish a positive direction Establish a positive direction Establish an origin (0 point) Establish an origin (0 point) The origin and positive direction must remain the same for the entire problem The origin and positive direction must remain the same for the entire problem

6. Sample Problem Page 17, Figure 2-2 Page 17, Figure 2-2 Set up a coordinate system Set up a coordinate system –Choose your own origin –Choose the positive direction

7. Distance vs. Displacement Distance Distance –Total length of travel –Units: m, cm, mm, km Displacement Displacement –Change in position = final - initial –  x = x f - x i Greek letter “delta”…stands for “Change in”

8. Back to the sample problem… Page 17, Figure 2-2 Page 17, Figure 2-2 If you leave your friend’s house, go to the supermarket, and come home, find the: If you leave your friend’s house, go to the supermarket, and come home, find the: –Distance –Displacement

9. Another example… Suppose you leave the grocery store, stop at your house, go back to the grocery store, and then go to your friend’s house. Find the: Suppose you leave the grocery store, stop at your house, go back to the grocery store, and then go to your friend’s house. Find the: –Distance –Displacement

10. Last example… Suppose you walk from the grocery store to your friend’s house. Find the: Suppose you walk from the grocery store to your friend’s house. Find the: –Distance –Displacement

11. What does the negative mean? Remember that we set a certain direction as positive… Remember that we set a certain direction as positive… –Getting a negative simply means that we are in the opposite direction as the one we established as positive –This DOES NOT mean that a negative number is less than a positive value

12. Before we go any further… We need to consistently set up problems to make sure we’re following the right steps and make our work clear We need to consistently set up problems to make sure we’re following the right steps and make our work clear (And to receive full credit )

13. Sample Problem Setup Sketch of the Problem Data Table Values Unknown Variables Ex: t = 3s x i = 5 m x f = ? All Work Equations Used Step by-step derivations (Not division, multiplication, etc)

14. It takes practice… It will take practice to start setting up problems (and not just jumping in to solving them) It will take practice to start setting up problems (and not just jumping in to solving them) In the end, you’ll be more accurate In the end, you’ll be more accurate You MUST set up problems like this on ALL tests, homework assignments, classwork, etc to receive full credit! You MUST set up problems like this on ALL tests, homework assignments, classwork, etc to receive full credit!

15. Speed vs. Velocity Speed Speed –Rate of motion –Units: m/s, km/hr Velocity Velocity –Displacement per unit of time –Units: m/s, km/hr  WITH a direction –N, S, E, W, etc –+ or --

16. Sample Problem You drive 4.0 hr at 30.0 mph and then another 4.0 hr at 50 mph. Is your average speed: You drive 4.0 hr at 30.0 mph and then another 4.0 hr at 50 mph. Is your average speed: –Greater than 40 mph –Equal to 40 mph –Less than 40 mph

17. Find average speed and average velocity for each part of the trip t = 10 s t = 50 s

18. One way to look at position vs. time…

19. Another way…

20. Practice problem #1 Draw a position vs. time graph for the following situation: Draw a position vs. time graph for the following situation: –You walk 2 m from your house in 3 seconds –You walk another 3 m in 5 seconds –You stop for 4 seconds to rest –You turn around and walk back to your house in 6 seconds

21. Answer…

22. Practice problem #2 Draw a position vs. time graph for the following situation: Draw a position vs. time graph for the following situation: –You walk 10 m toward the school in 5 seconds –You stop to answer your phone for 10 seconds –You walk back to your car in 5 seconds –You’re late for 1 st pd, so you walk to the 10 m to school in 3 seconds.

23. Answer…

24. Instantaneous Speed & Velocity Instantaneous Speed Instantaneous Speed –Magnitude of the instantaneous velocity Instantaneous Velocity Instantaneous Velocity –Velocity at one instant in time –Unit: m/s

25. Speedometer Question What does a car’s speedometer measure? What does a car’s speedometer measure? –Average Speed –Average Velocity –Instantaneous Speed –Instantaneous Velocity Explain. Explain.

26. Acceleration The change of velocity with time The change of velocity with time Units: m/s 2, mph/s, etc… Units: m/s 2, mph/s, etc…

27. Practice Problem #1 Saab advertises a car that goes from 0 to 60 mph in 6.2 seconds. Find the average acceleration. Saab advertises a car that goes from 0 to 60 mph in 6.2 seconds. Find the average acceleration.

28. Practice Problem #2 An airplane has an average acceleration of 5.6 m/s 2 during takeoff. How long does it take for the plane to reach a speed of 150 mph? An airplane has an average acceleration of 5.6 m/s 2 during takeoff. How long does it take for the plane to reach a speed of 150 mph?

29. Acceleration vs. Deceleration Acceleration Acceleration –Final speed > Initial Speed Deceleration Deceleration –Final speed < Initial Speed

30. Connection between acceleration and velocity Situation 1: Situation 1: –Acceleration and velocity in same direction –Speed of object increases Situation 2: Situation 2: –Acceleration and velocity in different directions –Speed of object decreases

31. Practice Problem #1 A ferry makes a short run between two docks. As the ferry approaches the dock (positive x-direction), it has a speed of 7.4 m/s and slows down to a stop in 12.3 s. Find the acceleration. A ferry makes a short run between two docks. As the ferry approaches the dock (positive x-direction), it has a speed of 7.4 m/s and slows down to a stop in 12.3 s. Find the acceleration.

32. Practice Problem #2 The ferry now leaves the dock As the ferry approaches the dock, it has a speed of 7.3 m/s and now slows down to a stop in 13.1 s. Find the acceleration. The ferry now leaves the dock As the ferry approaches the dock, it has a speed of 7.3 m/s and now slows down to a stop in 13.1 s. Find the acceleration. Hint: Think about positive/negative direction based on last problem

33. The most important acceleration… Recall from other science classes that gravity is always pulling down on everything. Recall from other science classes that gravity is always pulling down on everything. Gravity has an acceleration represented by: g Gravity has an acceleration represented by: g g = 9.81 m/s 2 g = 9.81 m/s 2 You need to use this exact value

34. Section B: Kinematics Equations Corresponding Book Sections: Corresponding Book Sections: –2.5, 2.6, 2.7 PA Assessment Anchors: PA Assessment Anchors: –S11.C.3

35. Motion with Constant Acceleration Object is either speeding up or slowing down Object is either speeding up or slowing down Object is just speeding up / slowing down at a constant rate (same acceleration at all times) Object is just speeding up / slowing down at a constant rate (same acceleration at all times)

36. Velocity as a function of time: Position as a function of time: Velocity as a function of position: Kinematics Equations

37. How do I know when to use each equation? That’s where the sketch and data table will come in handy… That’s where the sketch and data table will come in handy… Look at what you have, what you’re looking for, and find the equation that will include all of those variables Look at what you have, what you’re looking for, and find the equation that will include all of those variables You may need to use more than one equation in a problem You may need to use more than one equation in a problem

38. Practice Problem #1 A ball is thrown straight upward with an initial velocity of 8.2 m/s. If the acceleration of the ball is that of gravity, find the velocity after: A ball is thrown straight upward with an initial velocity of 8.2 m/s. If the acceleration of the ball is that of gravity, find the velocity after: –0.50 s –1.0 s

39. Practice Problem #2 A boat moves slowly inside a marina with a constant speed of 1.50 m/s. As soon as it leaves the marina, it accelerates at 2.40 m/s 2. Find the: A boat moves slowly inside a marina with a constant speed of 1.50 m/s. As soon as it leaves the marina, it accelerates at 2.40 m/s 2. Find the: –Speed it’s moving after 5.0 s –Distance it’s traveled after 5.0 s of acceleration

40. Practice Problem #3 A drag racer starts from rest and accelerates at 7.40 m/s 2. How far has it traveled in: A drag racer starts from rest and accelerates at 7.40 m/s 2. How far has it traveled in: –1.0 s –2.0 s –3.0 s

41. Review of the Equations…

42. Freely Falling Objects Free Fall -- the motion of an object falling only under the influence of gravity. Free Fall -- the motion of an object falling only under the influence of gravity. An object is in free fall the moment it is released, whether it’s thrown upward, downward, or just dropped. An object is in free fall the moment it is released, whether it’s thrown upward, downward, or just dropped. Why don’t we have true free fall on Earth? Why don’t we have true free fall on Earth?

43. Consider…

44. More on gravity Remember… Remember… –Acceleration due to gravity = g = 9.81 m/s 2 That value will be: That value will be: –Positive if our coordinate system has set down as positive –Negative if our coordinate system has set up as positive Gravity ALWAYS acts in the downward direction. Gravity ALWAYS acts in the downward direction. + +

45. Free fall from rest

46. Projectile Motion