DISPLACEMENT AND VELOCITY

1. DISPLACEMENT AND VELOCITY Chapter 2-1

2. Objectives • Describe motion in terms of frame of reference, displacement, time and velocity. • Calculate displacement, velocity and time interval. • Interpret position vs. time graphs.

3. Kinematics deals with the concepts that are needed to describe motion. • Dynamics deals with the effect that force shave on motion. • Together, kinematics and dynamics form the branch of physics known as Mechanics.

4. Describing Motion: this slide is not in your notes! • Are these two motions different?

5. 2.1 Displacement • As any object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called displacement. • Displacement is the change in position of an object. • Displacement doesn’t always tell you distance an object moved. • Displacement = final position – initial position • ∆x = xf-xo • Si units – meters (m)

6. 2.1 Displacement • Displacement is not always equal to the distance traveled. • Displacement can be positive or negative. • If displacement is positive, the object moves to the right. • If the displacement is negative, the object moves to the left.

7. 2.1 Displacement

8. 2.1 Displacement

9. 2.1 Displacement

10. 2.1 Displacement

11. 2.2 Speed and Velocity Average speed is the distance traveled divided by the time required to cover the distance. SI units for speed: meters per second (m/s)

12. 2.2 Speed and Velocity Average velocity is the displacement divided by the elapsed time. SI units for velocity: meters per second (m/s)

13. 2.2 Speed and Velocity • Velocity gives both direction and magnitude (amount) while speed only gives the magnitude - no direction • Average velocity does not tell you the speed or velocity of the moving object at each moment. • Average velocity can be positive or negative depending on direction moved. • Time can never be negative!

14. Average Velocity: • The slope of a position vs. time graph is called the average velocity.

15. Average Velocity: • Steeper slope means a faster moving object.

16. Speed and velocity: • Velocity and speed can be used interchangeably in everyday language • In Physics, however, there is a distinction: • Speed is a Scalar quantity (numerical value = magnitude only) • Velocity is Vector quantity - Describes motion with both direction and a numerical value (magnitude and direction)

17. Constant Velocity Model: Velocity vs. Time Graph • With constant velocity, • On a graph of velocity vs. time, displacement can be calculated by finding the area under the graph. • If the velocity is negative, the displacement calculate will be negative.

18. Constant Velocity Model: Velocity vs. Time Example • Use the graph to calculate the displacement of the object: • From 0 s to 3 s • From 3 s to 6 s • From 6 s to 9 s • From 0 s to 9 s

19. More practice:- ‘GUESS’ method • A vehicle travels 2345 m in 315 s toward the evening sun. What is its velocity? • Given: Displacement = 2345 m , time = 315 s • Unknown: Velocity = ? • Equation and model: v = D/t (kinematics) • Separate the unknown: ----- • Substitute and solve: V = 2345 / 315 • 7.44 m/s • does the answer make sense? • Yes!!

20. I will not accept late work Class assignment / Homework

21. Acceleration Section 3

22. Displacement for constant acceleration • The displacement from time 0 to time t is the area under the velocity graph from 0 to t. • Area = ½ b h v (m/s) t (s)

23. Displacement for constant acceleration • If we don’t know v, we can calculate it from a. • Area =l w + ½ b h v (m/s) t (s)

24. Instantaneous Velocity The instantaneous velocity indicates how fast the car moves and the direction of motion at each instant of time.

25. 2.3 Acceleration • The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs. • Accelerationis the measure of how fast something speeds up or slows down

26. 2.3 Acceleration DEFINITION OF AVERAGE ACCELERATION SI units for acceleration: (m/s2)

27. 2.3 AccelerationExample 3: Acceleration and Increasing Velocity • Determine the average acceleration of the plane. • G: • U: • E: (kinematics) • S: • S:

28. 2.3 Acceleration

29. 2.3 AccelerationExample 3: Acceleration and decreasing Velocity • Calculate the average acceleration • G: • U: • E: (kinematics) • S: • S:

30. 2.3 Acceleration

31. Graph for speeding up motion - Acceleration • Everyday examples of such motion include: • Driving a car • Throwing a ball • Kids sliding at the playground

32. Changes in velocity: • Instantaneous acceleration: • Since in some situations, the acceleration of an object can be constant , as a result, it will be the same value at any instant of time. • The plus or minus sign before the number indicates the two possible directions for the acceleration vector when the motion is along a straight line.

33. Interpret The Graph Below:Distance vs. time The graph shows an object which is not moving (at rest).

34. Interpret The Graph Below:Distance vs. Time (constant velocity): The object is moving at a constant velocity (not changing).

35. Interpret The Graph Below:Distance vs. Time ( constant negative velocity) This object is moving with a constant velocity (negative – object moving in the opposite direction)

36. Interpret The Graph Below:Distance vs. Time (acceleration) The curve in the graph shows that the objects velocity is changing as time passes. This is acceleration.

37. Interpret The Graph Below:Distance vs. Time (deceleration) The curve in the graph shows that the objects velocity is decreasing as time passes. The object is decelerating

38. Interpret The Graph Below:Distance vs. Time In the first part of the graph the object is moving with constant velocity. In the second part of the graph the object is at rest (not moving). In the third part the object is again moving with constant velocity.

39. Interpret The Graph Below::Velocity vs. Time (constant velocity) The objects velocity does not change as time passes. Constant velocity.

40. Interpret The Graph Below:Velocity vs. Time (constant acceleration) The objects velocity is increasing as time passes – it is accelerating. The straight line shows that it is constant acceleration.

41. Interpret The Graph Below:Velocity vs. Time (constant acceleration - negative) The objects velocity is decreasing as time passes – it is decelerating / slowing down The straight line shows that it is constant deceleration.

42. 2.4 Equations of Kinematics for Constant Acceleration For one dimensional motion it is customary to dispense with the use of boldface symbols overdrawn with arrows for the displacement, velocity, and acceleration vectors. We will, however, continue to convey the directions with a plus or minus sign.

43. 2.4 Equations of Kinematics for Constant Acceleration Equations of Kinematics for Constant Acceleration

44. 2.4 Equations of Kinematics for Constant Acceleration • G: • U: • E: (kinematics) • S: • S:

45. 2.4 Equations of Kinematics for Constant Acceleration Example 6 Catapulting a Jet Find its displacement.

46. 2.4 Equations of Kinematics for Constant Acceleration • G: • U: • E: (kinematics) • S: • S:

47. I will not accept late work Class assignment / Homework

48. Chapter 2 Section 6: Falling Objects

49. Free Fall acceleration: • An object thrown or dropped in the presence of Earth’s gravity experiences a constant acceleration directed toward the center of the earth. • This acceleration is called the free- fall acceleration, or the acceleration due to gravity. • Free fall acceleration is the same for all objects, regardless of their mass.

50. Free fall acceleration: • The value for free fall acceleration used in this book is: • g = 9.81 m/s2. • In this book, the direction of the free fall acceleration is considered to be negative because the object accelerates toward earth. Positive Negative