1. One Dimensional Motion
Section 1 Displacement and Velocity
Chapter 2
One Dimensional Motion
To simplify the concept of motion, we will first consider motion that takes place in one direction.
One example is the motion of a commuter train on a straight track.
To measure motion, you must choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time.

2. displacement = final position – initial position
Section 1 Displacement and Velocity
Chapter 2
Displacement
Displacement is a change in position.
Displacement is not always equal to the distance traveled.
The SI unit of displacement is the meter, m.
Dx = xf – xi
displacement = final position – initial position

3. Positive and Negative Displacements
Section 1 Displacement and Velocity
Chapter 2
Positive and Negative Displacements

4. Chapter 2 Average Velocity
Section 1 Displacement and Velocity
Chapter 2
Average Velocity
Average velocity is the total displacement divided by the time interval during which the displacement occurred.
In SI, the unit of velocity is meters per second, abbreviated as m/s.

5. Chapter 2 Velocity and Speed
Section 1 Displacement and Velocity
Chapter 2
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.

6. Interpreting Velocity Graphically
Section 1 Displacement and Velocity
Chapter 2
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

7. Interpreting Velocity Graphically, continued
Section 1 Displacement and Velocity
Chapter 2
Interpreting Velocity Graphically, continued
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.

8. Chapter 2 Changes in Velocity
Section 2 Acceleration
Changes in Velocity
Acceleration is the rate at which velocity changes over time.
An object accelerates if its speed, direction, or both change.
Acceleration has direction and magnitude. Thus, acceleration is a vector quantity.

9. Changes in Velocity, continued
Chapter 2
Section 2 Acceleration
Changes in Velocity, continued
Consider a train moving to the right, so that the displacement and the velocity are positive.
The slope of the velocity-time graph is the average acceleration.
When the velocity in the positive direction is increasing, the acceleration is positive, as at A.
When the velocity is constant, there is no acceleration, as at B.
When the velocity in the positive direction is decreasing, the acceleration is negative, as at C.

10. Relationship Between Acceleration and Velocity
Chapter 2
Relationship Between Acceleration and Velocity
Uniform velocity (shown by red arrows maintaining the same size)
Acceleration equals zero

11. Relationship Between Velocity and Acceleration
Chapter 2
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)

12. Relationship Between Velocity and Acceleration
Chapter 2
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)

13. Kinematic Equations
a = Δ v = vf - vi ti = 0
Δ t tf - ti
Therefore
vf = vi at

14. Kinematic Equations Vavg = Δx t Δx = vavgt = vi + vf t 2
Δx = ½ (vi + vf) t
But vf = vi at
Δx = ½ (vi + vi at) t
Δx = vi t + ½ at2

15. Kinematic Equations Δx = ½ (vi + vf) t
We can develop an equation without t
vf = vi at
t = vf - vi (sub. into equation above for ΔX) a
vf2 = vi aΔx

16. x a 2 v at 1 t D + = ÷ ø ö ç è æ Kinematic Equations
Summary Uniform Acceleration equations of motion x a 2 v at 1 t i f
average D + = ÷ ø ö ç è æ

17. Velocity and Acceleration
Chapter 2
Section 2 Acceleration
Velocity and Acceleration

18. 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

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

20. 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
vi= 0
a = g

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

22. 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