1. ST.JOSEPH'S HIGHER SECONDARY SCHOOL
TVM-1
DEPARTMENT OF PHYSICS
WELCOMES
YOU

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

3. Table of Contents Position and Displacement Velocity Acceleration
Motion with Constant Acceleration
Falling Objects
Equations for Chapter 2

4. One-Dimensional Motion
The simplest kind of motion
Things can move forward and backward, but not left and right

5. in a certain direction, not the total distance traveled
The Big Idea
Displacement is
a change of position
in a certain direction, not
the total distance traveled

6. Read the TIP at the bottom of p.41!
Displacement
When things start moving, the length of a straight line drawn from the object’s initial position to it’s final position is it’s displacement
In one dimension…
Change in position along x-axis = (final position on x-axis) – (initial position on x-axis)
Read the TIP at the bottom of p.41!

7. Equations for Chapter 2

8. More Equations…

9. Keep in mind…
Displacement is not always equal to the distance traveled!
Displacement can be positive or negative!

10. POSITIVE AND NEGATIVE QUANTITIES ARE JUST DIRECTIONS IN MOTION PROBLEMS!

11. Velocity
It is the time rate of change of displacement

12. Average Velocity
Average velocity is the total displacement divided by the time interval during which the displacement occurred.

13. Velocity and Speed
Velocity describes motion with both a direction and a numerical value
(a magnitude).
Speed has no direction, only magnitude.
Average speed is equal to the total distance traveled divided by the time interval.

14. Velocity and Speed

15. +’s and –’s are Directional!

16. Interpreting Velocity Graphically
For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph.
If the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity.
Object 1: positive slope = positive velocity
Object 2: zero slope= zero velocity
Object 3: negative slope = negative velocity

17. Instantaneous Velocity
The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.
The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.

18. Acceleration is “rate of change of velocity with respect to time”
How much does your velocity change, and how fast does this happen?
a is measured in m/s2

19. Just like Velocity Acceleration is a vector quantity
Has both a magnitude (speed) AND direction
Can be positive or negative
JUST DIRECTIONAL!!!

20. Graphs can tell us things

21. Review of last week Position: where are you at?
Displacement: change in position
Velocity: rate of change in position
Acceleration: rate of change of velocity

22. Velocity vs. Time

23. v with constant a
Rearranging the equation tells us that…

24. Finding displacement Let’s substitute our new equation in for vf …
…and simplify the new equation.

25. One last equation…

26. One Dimensional Motion

27. Terms Displacement vs. Distance
Displacement: Change in position (vector)
Distance: How far an object has travelled (scalar)
Symbol: Δx or Δx
SI Unit: meter, m

28. Position

29. Terms Velocity vs. Speed
Velocity: Rate of the change in position (vector)
Speed: Rate of distance covered (scalar)
Symbol: v or v
SI Unit: meter per second, m/s

30. Average Velocity

31. Instantaneous Velocity

32. Acceleration vs. Acceleration
Terms
Acceleration vs. Acceleration
Acceleration: The rate at which velocity changes (vector)
Acceleration: The rate at which speed changes (scalar)
Symbol: a or a
SI Unit: meters per second per second or meters per second squared, m/s/s or m/s2

33. Average Acceleration

34. Instantaneous Acceleration

35. Position vs. Time Graph

36. What are the velocities?

37. What are the velocities?

38. Average Velocity on an x-t graph

39. vav vs vinst on an x-t graph

40. x-t graph vs motion of a particle

41. Instantaneous Velocity on an x-t graph

42. Velocity vs. Time Graph
The slope of a v vs. t graph is the acceleration
The area between the curve and the horizontal axis of a v vs. t graph is the displacement

43. Comparison of v-t to a-t graphs

44. Instantaneous Acceleration vs Average Acceleration from a v-t graph

45. v-t graph vs motion of a particle

46. x-t graph vs motion of a particle with acceleration

47. What are the accelerations and displacements?

48. What are the accelerations and displacements?

49. Acceleration vs. Time Graph
The slope means NOTHING
The area between the curve and the horizontal axis is the change in velocity a
10 s t
-10 m/s/s

50. Important Acceleration tells us how fast velocity changes
Velocity tells us how fast position changes

51. Kinematics Equations (accelerated motion)

52. Falling Bodies, thrown up objects, and the y-direction
All things fall at the same rate (neglecting air resistance)
On earth that rate is 9.80 m/s2
That rate is an acceleration
The name of that acceleration is Gravity

53. Object moving in y-direction

54. Changing Acceleration

55. Velocity by Integration

56. Position by Integration

57. THANK YOU