AP Physics Kinematics 1D/2D: Description of Motion

1. AP PhysicsKinematics 1D/2D: Description of Motion

2. Homework for Chapter 2 • Read Chapter 2 • HW 2.A : pp. 57-59: 8,9,12,13,16,17,20,26,34,35,38,39. • HW 2.B: pp. 60-61: 46,47,48,50,52, 58,59,61,70,71,72-75,80.

3. Learning Objectives for Chapter 2 • Students will understand the general relationships among position, velocity, and acceleration for the motion of a particle along a straight line so that given a graph of one of the kinematics quantities, position, velocity, or acceleration, as a function of time, they can: • recognize in what time intervals the other two are positive, negative, or zero. • identify or sketch a graph of each as a function of time. • Students will understand the special case of motion with constant acceleration so they can: • write down expressions for velocity and position as functions of time. • identify or sketch graphs of these quantities.

4. Warmup: Movin’ On Acceleration refers to any change in an object’s velocity. Velocity not only refers to an object’s speed but also its direction. The direction of an object’s acceleration is the same as the direction of the force causing it. *************************************************************** Complete the table below by drawing arrows to indicate the directions of the objects’ velocity and acceleration.

5. Scalar Quantities • distance – the total path length in traveling from one position to another. • example: • • Distance is a scalar quantity. • • scalar quantity – only has magnitude (size), not direction. • • remember to include units! • examples of scalars: • • 150 kg

6. Scalar Quantities • speed – the rate at which distance is travelled • • Speed is a scalar quantity • • SI units: m/s • • average speed – distance divided by time ave. sp. = d • t • • instantaneous speed – how fast something is moving at a particular instant in time • example: your car speedometer

7. Motion is Relative • There's no such thing as absolute speed. • Speed only has meaning when it is measured relative to some fixed point. • Don't believe me? How fast is the cannonball to the right moving?

9. Huh? Two kinds… Inertial frame of reference is a reference frame in which an object stays either at rest or at a constant velocity unless another force acts upon it. When a body does not seem to be acting in accordance with inertia, it is in a non-inertial frame of reference or accelerating.

10. Vector Quantities • displacement – how far and in what direction • displacement is a vector • vector quantity – has magnitude AND direction • represented by arrows • the length of the arrow represents the magnitude

11. One-Dimensional Displacement and Velocity: Vector Quantities velocity – how fast something is moving and in what direction • speed is a scalar; velocity is a vector • SI units are m/s average velocity = displacement time v = Δ x = x – xoor v = x or x = v t Δ t t – to t instantaneous velocity – how fast something is moving, and in what direction at a particular instant in time

12. Vector Quantities Check for Understanding:

14. Vector Quantities

16. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities

18. Motion Graphs Position vs. Time Graphs Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s. Consider a car moving with a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating.

19. Motion Graphs Position vs. Time Graphs

20. Motion Graphs Position vs. Time Graphs x1 Δ x x2 Δ t t1 t2 To find instantaneous velocity, find the slope of the tangent at a point on the curve. v = slope = Δ x Δ t To find average velocity during a time period: v = x2 – x1 t2 – t1

21. Motion Graphs Check for Understanding: Use the principle of slope to describe the motion of the objects depicted by the two plots below. 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. Be complete in your description.

22. Did you get it all? Position vs. Time Graphs: Check for Understanding Practice A: The object has a positive or rightward velocity (note the + slope). The object has a changing velocity (note the changing slope); it is accelerating. The object is moving from slow to fast since the slope changes from small big. Practice B: The object has a negative or leftward velocity (note the - slope). The object has a changing velocity (note the changing slope); it has an acceleration. The object is moving from slow to fast since the slope changes from small to big.

23. Let’s make a foldable Motion Graph

24. Kinematic Graphs Position, Velocity, & Acceleration vs. Time AP Physics

25. What does each graph represent? • X vs. T = position vs. time • V vs. T = velocity vs. time • A vs. T = acceleration vs. time

26. Important points to remember… • X vs. T graphs: • The slope of a position vs. time graph is the velocity. • A linear x vs. t graph indicates constant velocity. • A curvy x vs. t graph indicates that the velocity is changing ( the object is accelerating).

27. Important points to remember… • X vs. T graphs: • If the graph is curvy, use a pencil as a tangent line. • If the slope of the tangent line is getting more positive, then the velocity is getting more positive. • If it is more negative, then the velocity is more negative.

28. Important points to remember… • V vs. T graphs: • The slope of a velocity vs. time graph is the acceleration. • The area under a velocity vs. time is the change of position (Δx, also known as displacement). • If the velocity is getting closer to zero, then the object is slowing down. • Velocity graphs will be linear, because we will only be studying objects with constant acceleration.

29. Important points to remember… • A vs. T graphs: • The area under an acceleration vs. time is the change of velocity (Δv). • Acceleration vs. time graphs will be horizontal for us, because we will only be studying objects which have a constant acceleration.

30. Example 1 • Notice the x vs. t graph starts with a “not steep” slope and it gets steeper (more positive). • We would say that this indicates that the object begins slowly (at rest) and get faster as it moves to the right (positive direction)

31. Example 1 • This mean the v vs. t graph should begin at zero (v = 0) and get more positive.

32. Example 1 • The a vs. t graph is the slope of the v vs. t graph. • Positive slope on v vs. t means a constant positive acceleration.

33. Example 2 • Notice the x vs. t graph starts with a “steep, positive” slope and it gets less steep (more negative). • We would say that this indicates that the object begins very quickly and gets slower as it moves to the right (positive direction)

34. Example 2 • This means the v vs. t graph should begin at some positive value, and get closer and closer to zero ( more negative).

35. Example 2 • The a vs. t graph is the slope of the v vs. t graph. Negative slope on the v vs. t means a constant Negative acceleration.

36. Example 3 • The x vs. t graph starts with a “ not steep” slope and it gets steeper (more and more negative). • This indicates that the object begins very slowly (at rest) and gets faster as it moves to the left (negative direction).

37. Example 4 • The x vs. t graph starts with a “steep, negative” slope and it gets less steep (more positive). • The object begins very quickly and gets slower and slower as it moves to the left (negative direction)

38. Example 4 • This means the v vs. t graph should begin at some negative value, and get closer and closer to zero ( more positive)

39. Example 4 • Positive slope on v vs. t graph means a constant positive acceleration.

40. Example 5More Complex • The object begins at rest and gets faster. Then the object moves with a constant velocity.

41. Example 5More Complex • The object begins at rest and gets faster. Then the object is moving to the right and it slows down ending with a velocity of zero.

42. Acceleration acceleration – the time rate of change of velocity • acceleration is a vector quantity; SI units are m/s2 average acceleration = change in velocity change in time a = Δ v = v – voor a = v – vo Δ t t – to t instantaneous acceleration – the acceleration at a particular instant in time

44. Acceleration Velocity vs. Time Graphs Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s. Consider a car moving with a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating.

45. 2.3 Acceleration Velocity vs. Time Graphs The area under the curve on a velocity vs. time graph represents displacement.

46. Acceleration Velocity vs. Time Graphs -x Signs of Velocity and Acceleration +x

47. Acceleration Velocity vs. Time Graphs Acceleration vs. Time Graphs – draw for each of the above Acceleration - 0 + Acceleration - 0 + Acceleration - 0 + Acceleration - 0 + Time Time Time Time

48. Acceleration

50. Acceleration Check for Understanding: Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true): • moving in the positive direction. • moving with a constant velocity. • moving with a negative velocity. • slowing down. • changing directions. • speeding up. • moving with a positive acceleration. • moving with a constant acceleration.