Motion

1. Motion

2. Unit 1: MotionChapter 2: Describing Motion • 2.1 Position, Velocity, and Acceleration • 2.2 Position vs. Time Graphs • 2.3 Velocity vs. Time Graphs

3. Key Question: How are position, speed, and velocity related? 2.1 Investigation: Position, Speed, and Velocity Objectives: • Measure positive and negative positions. • Measure positive and negative velocity. • Compare speed and velocity.

4. Position, Velocity, and Acceleration • Position is a variable. • Position and distance are similar but not the same. Both use units of length. • Position is given relative to an origin. If a car moves 20 cm, what is it’s new position?

5. Position and displacement • A change in position is called displacement. • A displacement of –20 cm means the car leaves the 50-cm mark and moves toward the origin. • A displacement of 20 cm means the car moves away from the origin.

6. Velocity • The velocityof an object (v) tells you both its speed and its direction of motion. • Velocity can be positive or negative, so it includes information about the moving object’s direction. • Constant velocitymeans that both the speed and the direction an object is traveling remains constant.

7. Positive velocity • The sign for velocity is based on the calculation of a change in position. • The change in position is the final position minus the initial position.

8. Negative velocity • Negative velocity means the position is decreasing relative to the starting point.

9. Velocity

10. Average and instantaneous velocity • Average velocityis the total displacement divided by the total time taken. • Instantaneous velocitydescribes the velocity of an object at one specific moment in time or at one specific point in its path.

11. Relative velocity • Relative velocitydescribes the velocity of an object with respect to a frame of reference. • If you are sitting in a chair, you are not moving relative to Earth, but you are moving at about 67,000 mph relative to the Sun.

12. Using relative velocity A people mover has a velocity of 1 m/s and is 150 m long. If a man walks 2 m/s relative to the people mover, how long will it take him to reach the opposite end if he walks in the direction that the people mover travels? • Looking for: …the time in seconds. • Given:… velocity of the people mover (1 m/s), the relative velocity of the walker (2 m/s), and the displacement (150 m). • Relationship:Use this version of the velocity equation: t = Δx ÷ v • Solution: t = 150 m ÷ (1 m/s + 2 m/s) = 150 m ÷ 3 m/s = 50 s

13. Acceleration • Accelerationis the rate at which velocity changes.

14. Acceleration • Acceleration and velocity are completely different ways to describe an object’s motion. • An object can be accelerating when its velocity is zero. • Like velocity, acceleration can be positive or negative. • An object will have a positive acceleration when it is speeding up in the positive direction, and when it is slowing down in a negative direction.

15. Calculating acceleration

16. Calculating acceleration A sailboat moves at 1 m/s. Wind increases its velocity to 4 m/s in 3 seconds. Calculate the acceleration. • Looking for:.. the acceleration in m/s/s. • Given:… the initial velocity (vi=1 m/s), final velocity (vf=4 m/s), and time (t=3 s) • Relationship:Use: a = (vf – vi) ÷ t • Solution: a = 4 m/s – 1 m/s = 3 m/s = 1 m/s 3 s 3 s

18. Units of acceleration • An acceleration in “meters per second per second (m/s/s) is often written m/s2 or meters per second squared.

19. Unit 1: MotionChapter 2: Describing Motion • 2.1 Position, Velocity, and Acceleration • 2.2 Position vs. Time Graphs • 2.3 Velocity vs. Time Graphs

20. Key Question: How are graphs used to describe motion? 2.2 Investigation: Position, Velocity, and Time Graphs Objectives: • Create graphs of velocity versus position and time. • Create a predictive model for the velocity of car rolling down a hill.

21. Position vs. Time Graphs • Motion graphs are an important tool used to show the relationships between position, velocity, acceleration, and time. • Graphs help test drivers and engineers see how much of the straight track each car covered in equal time intervals. • Drivers can make adjustments in how they operate cars.

22. Slope • The slope of a line is the ratio of the “rise,” or vertical change, to the “run,” or horizontal change. • The rise is equal to the height of the triangle. • The run is equal to the length along the base of the triangle.

24. Position vs. Time Graphs • A position vs. time graph can tell you whether an object’s velocity is constant or changing. (Both cars have constant velocity, but Car A is faster than Car B.) • If the velocity is constant, the graph is a straight line with a constant slope.

25. Position vs. time graphs of accelerated motion • If the velocity is changing, the slope changes, so the graph curves.

26. Position vs. time graphs of accelerated motion • The graph of an object slowing down is also curved. • An example is a car coming to a gradual stop at a red light.

28. Unit 1: MotionChapter 2: Describing Motion • 2.1 Position, Velocity, and Acceleration • 2.2 Position vs. Time Graphs • 2.3 Velocity vs. Time Graphs

29. Key Question: What happens to the velocity of an object as it moves downhill? 2.3 Investigation: Position, Velocity, and Time Graphs Objectives: • Explain the motion of the Energy Car, in terms of velocity and acceleration, as it moves along an inclined track. • Infer the meaning of acceleration from a velocity versus time graph. • Apply the acceleration formula to solve problems.

30. Velocity vs. time graphs • The velocity vs. time graph has velocity on the y-axis and time on the x-axis. • On this graph, constant velocity is shown with a straight horizontal line.

31. Velocity vs. time graphs • The velocity vs. time graph is the best tool for understanding acceleration. • It clearly shows how the velocity of an object changes with time.

32. Constant acceleration • The velocity vs. time graph shown is for a ball in free fall. • Since the ball is accelerated by gravity, it’s velocity increases by the same amount: 9.8 m/s2. • What is the velocity of the ball after 4 seconds? Ans: 29.4 + 9.8 = 39.2 m/s2 ,down

34. Constant acceleration • Don’t confuse constant velocity with constant acceleration. • Constant velocity means an object’s positionchanges by the same amount each second. • Constant acceleration means an object’s velocitychanges by the same amount each second.

35. Calculating acceleration • The slope of a velocity vs. time graph represents the acceleration of the object.

36. Calculating acceleration • The slope of a graph is equal to the ratio of rise to run. • The riseis the amount the velocitychanges. • The run is the amount the time changes.

37. Calculating acceleration from a graph Calculate the acceleration shown on the graph. • Looking for:… the acceleration in m/s/s. • Given:… a graph of velocity vs. time • Relationship:The acceleration is equal to the slope of the line. • Solution: slope = rise = 40 m/s = 4 m/s2 run 10 s

38. Displacement • The velocity vs. time graph gives us a way to calculate the object’s displacement even when its velocity is changing. • The displacement is equal to the area on the graph.

39. Direction • To show direction on a velocity vs. time graph, we must include a portion of the graph that shows negative velocities.

40. Motion Graph Summary

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