1. Motion in One Dimension
Chapter 2
Motion in One Dimension

2. The aim of physics is to understand the rules by which nature plays
The aim of physics is to understand the rules by which nature plays. As participant-observers, we try to deduce the rules from our observations.
The success of our efforts will depend not only on our powers of observation but on what questions we ask and how carefully we formulate them

3. Dynamics
The branch of physics involving the motion of an object and the relationship between that motion and other physics concepts
Kinematics is a part of dynamics
In kinematics, you are interested in the description of motion
Not concerned with the cause of the motion

4. Matter in Motion
Develop a precise quantitative vocabulary to describe how things move.
Look for rules governing these forces or interactions and their effect on motion.
We will investigate how the universe works by studying the motions and interactions of its parts, much as if it were a great machine.
The study of forces and motion in nature is called mechanics.

5. Brief History of Motion
Sumaria and Egypt
Mainly motion of heavenly bodies
Greeks
Also to understand the motion of heavenly bodies
Systematic and detailed studies

6. “Modern” Ideas of Motion
Galileo
Made astronomical observations with a telescope
Experimental evidence for description of motion
Quantitative study of motion

7. A Vocabulary for describing Motion
Instants and Intervals:
Interval ≡ difference between two instants

8. A Vocabulary for describing Motion
Point Objects: An object small enough such that it can be thought of as a point.
The size of the object can be neglected with respect to the distance of object’s traveling

9. A Vocabulary for describing Motion
Positions and Distances:
Position: any point or point object is assigned its coordinates on some set of coordinate axes.
Displacement:
Distance:

10. Position Defined in terms of a frame of reference
One dimensional, so generally the x- or y-axis

11. Vector Quantities
Vector quantities need both magnitude (size) and direction to completely describe them
Represented by an arrow, the length of the arrow is proportional to the magnitude of the vector
Head of the arrow represents the direction
Generally printed in bold face type

12. Scalar Quantities
Scalar quantities are completely described by magnitude only

13. Displacement Measures the change in position
Represented as x (if horizontal) or y (if vertical)
Vector quantity
+ or - is generally sufficient to indicate direction for one-dimensional motion
Units are meters (m) in SI, centimeters (cm) in cgs or feet (ft) in US Customary

15. Displacements

16. Distance
Distance may be, but is not necessarily, the magnitude of the displacement
Blue line shows the distance
Red line shows the displacement

17. Example 2-1 a. Find the displacement from a position of 500m to a position of 300 m. b. Find the displacement from a position of -500m to a position of -300 m. c. Find the distance traveled.

18. A Vocabulary for describing Motion
Average Velocity:

19. Velocity It takes time for an object to undergo a displacement
The average velocity is rate at which the displacement occurs
generally use a time interval, so let ti = 0

20. Velocity continued
Direction will be the same as the direction of the displacement (time interval is always positive)
+ or - is sufficient
Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.)
Other units may be given in a problem, but generally will need to be converted to these

21. Speed Speed is a scalar quantity
same units as velocity
total distance / total time
May be, but is not necessarily, the magnitude of the velocity

22. Instantaneous Velocity
The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero
The instantaneous velocity indicates what is happening at every point of time

23. Uniform Velocity Uniform velocity is constant velocity
The instantaneous velocities are always the same
All the instantaneous velocities will also equal the average velocity

24. Graphical Interpretation of Velocity
Velocity can be determined from a position-time graph
Average velocity equals the slope of the line joining the initial and final positions
Instantaneous velocity is the slope of the tangent to the curve at the time of interest
The instantaneous speed is the magnitude of the instantaneous velocity

25. Average Velocity

26. Instantaneous Velocity

27. Acceleration
Changing velocity (non-uniform) means an acceleration is present
Acceleration is the rate of change of the velocity
Units are m/s² (SI), cm/s² (cgs), and ft/s² (US Cust)

28. Average Acceleration Vector quantity
When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing
When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

29. Instantaneous and Uniform Acceleration
The limit of the average acceleration as the time interval goes to zero
When the instantaneous accelerations are always the same, the acceleration will be uniform
The instantaneous accelerations will all be equal to the average acceleration

30. Graphical Interpretation of Acceleration
Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph
Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph

31. Average Acceleration

32. Relationship Between Acceleration and Velocity
Uniform velocity (shown by red arrows maintaining the same size)
Acceleration equals zero

33. Relationship Between Velocity and Acceleration
Velocity and acceleration are in the same direction
Acceleration is uniform (blue arrows maintain the same length)
Velocity is increasing (red arrows are getting longer)

34. Relationship Between Velocity and Acceleration
Acceleration and velocity are in opposite directions
Acceleration is uniform (blue arrows maintain the same length)
Velocity is decreasing (red arrows are getting shorter)

35. Kinematic Equations
Used in situations with uniform acceleration

36. Notes on the equations
Gives displacement as a function of velocity and time

37. Notes on the equations
Shows velocity as a function of acceleration and time

38. Graphical Interpretation of the Equation

39. Notes on the equations
Gives displacement as a function of time, velocity and acceleration

40. Notes on the equations
Gives velocity as a function of acceleration and displacement

41. Problem-Solving Hints
Be sure all the units are consistent
Convert if necessary
Choose a coordinate system
Sketch the situation, labeling initial and final points, indicating a positive direction
Choose the appropriate kinematic equation
Check your results

42. Free Fall
All objects moving under the influence of only gravity are said to be in free fall
All objects falling near the earth’s surface fall with a constant acceleration
Galileo originated our present ideas about free fall from his inclined planes
The acceleration is called the acceleration due to gravity, and indicated by g

43. Acceleration due to Gravity
Symbolized by g
g = 9.8 m/s²
g is always directed downward
toward the center of the earth

44. Free Fall -- an object dropped
Initial velocity is zero
Let up be positive
Use the kinematic equations
Generally use y instead of x since vertical
vo= 0
a = g

45. Free Fall -- an object thrown downward
a = g
Initial velocity  0
With upward being positive, initial velocity will be negative

46. Free Fall -- object thrown upward
Initial velocity is upward, so positive
The instantaneous velocity at the maximum height is zero
a = g everywhere in the motion
g is always downward, negative
v = 0

47. Thrown upward, cont. The motion may be symmetrical
then tup = tdown
then vf = -vo
The motion may not be symmetrical
Break the motion into various parts
generally up and down

48. Non-symmetrical Free Fall
Need to divide the motion into segments
Possibilities include
Upward and downward portions
The symmetrical portion back to the release point and then the non-symmetrical portion

49. Combination Motions