1. Describing Motion

2. the study of motion motion is a change in position two branches Mechanics

3. describes how objects move Kinematics Dynamics explains the causes of motion

4. Chapter 3 is about one- dimensional motion, as on a number line Mathematical Representations of Motion—The Basics

5. Origin: A reference point to the left—negative to the right—positive Mathematical Representations of Motion—The Basics

6. When motion is vertical: up—positive down—negative Mathematical Representations of Motion—The Basics

7. An object has moved if at one time its position is x 1 and at another time its position is x 2. Mathematical Representations of Motion—The Basics

8. An object’s position at a time can be represented by an ordered pair: (t 1, x 1 ) or (t 2, x 2 ) Mathematical Representations of Motion—The Basics

9. Displacement the change in position between two distinct points often different from the distance traveled

10. Scalars and Vectors a scalar contains just one piece of information a vector contains two: magnitude and direction vectors are represented in bold: d, v, etc.

11. Scalars and Vectors for vectors in one- dimensional motion, subscripts may be used, such as d x this will represent a change in position

12. What do we know about the family’s travels? a. displacement = 2 km north Since displacement is a vector, a direction must be indicated. Example 3-1

13. What do we know about the family’s travels? b. the car has traveled 10 km Since distance is a scalar, no direction needs to be indicated. Example 3-1

14. What do we know about the family’s travels? c. the displacement is zero, since its final and initial positions are the same When d = 0, no direction is necessary. Example 3-1

15. What do we know about the family’s travels? d. the car has traveled 20 km Example 3-1

16. plots ordered pairs of data in a simple form Position-time Graph

17. allows the calculation of: displacement average speed Position-time Graph

18. to calculate: Average Speed v = |x 2 - x 1 | t 2 - t 1 = s ΔtΔt = |Δx| ΔtΔt

19. the speed of an object at any one moment the slope of the position- time curve at that point Instantaneous Speed

20. The slope is easy to find if the position-time curve is linear, but what if it is a curve? We can use a tangent line. Instantaneous Speed

21. Can you see why graph (c) is the best estimate for a tangent line? Instantaneous Speed

22. Be sure to recognize the difference between average speed and instantaneous speed. For which one can you get a speeding ticket?? Instantaneous Speed

23. Velocity includes both speed and direction to calculate average velocity: v = d ΔtΔt

24. Velocity displacement ( d ) might be positive or negative in one-dimensional motion v = d ΔtΔt

25. Velocity can be calculated from a position-time graph can be positive or negative v = d ΔtΔt

26. allows the calculation of: acceleration Velocity-time Graph

27. Acceleration change in velocity with respect to time to calculate average acceleration: a = ΔvΔv ΔtΔt

28. Acceleration acceleration is a vector pointing in the same direction as Δ v a = ΔvΔv ΔtΔt

29. Acceleration average acceleration can be calculated as the slope of a velocity- time graph a = ΔvΔv ΔtΔt

30. Acceleration uniformly accelerated motion involves a constant rate of velocity change

31. Equations of Motion

32. First Equation of Motion often used if you want to know the final velocity when you know the initial velocity and acceleration v 2x = v 1x + a x Δt

33. Determining Displacement Algebraically d x = ½(v 1x + v 2x )Δt d x = v x Δt

34. Determining Displacement Geometrically the area “under the curve” of a velocity-time graph is equal to the displacement of the moving object

35. Second Equation of Motion two common forms: d x = v 1x Δt + ½a x (Δt)² x 2 = x 1 + v 1x Δt + ½a x (Δt)²

36. Third Equation of Motion two common forms: d x = v 2x ² – v 1x ² 2a x x 2 = x 1 + v 2x ² – v 1x ² 2a x

37. Equations of Motion These are used to solve most problems involving straight-line, constant acceleration motion. Sometimes there will be more than one possible method.

38. Free Fall an object falls under the influence of gravity alone with negligible air resistance near earth’s surface: g = g y = -9.81 m/s²

39. Free Fall the equations of motion are easily adapted by replacing the acceleration with g y : v 2y = v 1y + g y Δt First Equation of Motion:

40. Free Fall Second Equation of Motion: d y = v 1y Δt + ½g y (Δt)² Third Equation of Motion: 2g y d y = v 2y ² – v 1y ²