Forces and motion 2

1. FORCES AND MOTION 2
PHYSICS 30

2. DESCRIBING MOTION WITH DIAGRAMS
• The two most commonly used types of diagrams used to describe the motion of objects are:
Ticker Tape Diagrams
Vector Diagrams

3. TICKER TAPE DIAGRAMS
• A common way of analyzing the motion of objects in physics labs is to perform a ticker tape analysis. A
long tape is attached to a moving object and threaded through a device that places a tick upon the tape
at regular intervals of time - say every 0.10 second. As the object moves, it drags the tape through the
"ticker," thus leaving a trail of dots. The trail of dots provides a history of the object's motion and
therefore a representation of the object's motion.

4. TICKER TAPE DIAGRAMS
• The distance between dots on a ticker tape represents the object's position change during that time
interval. A large distance between dots indicates that the object was moving fast during that time
interval. A small distance between dots means the object was moving slow during that time interval.

5. TICKER TAPE DIAGRAMS
• The analysis of a ticker tape diagram will also reveal if the object is moving with a constant velocity or
accelerating. A changing distance between dots indicates a changing velocity and thus an acceleration.
A constant distance between dots represents a constant velocity and therefore no acceleration.

6. TICKER TAPE DIAGRAMS
• Ticker tape diagrams are sometimes referred to as oil drop diagrams. Imagine a car with a leaky engine
that drips oil at a regular rate. As the car travels through town, it would leave a trace of oil on the street.
That trace would reveal information about the motion of the car.
• Examples

7. VECTOR DIAGRAMS
• Vector diagrams are diagrams that depict the direction and relative magnitude of a vector quantity by a
vector arrow. Vector diagrams can be used to describe the velocity of a moving object during its motion.
For example, a vector diagram could be used to represent the motion of a car moving down the road.

8. VECTOR DIAGRAMS
• In a vector diagram, the magnitude of a vector quantity is represented by the size of the vector arrow. If
the size of the arrow in each consecutive frame of the vector diagram is the same, then the magnitude
of that vector is constant. The diagrams below depict the velocity of a car during its motion.

9. POSITION-TIME GRAPHS
• Contrasting a Constant and a Changing Velocity
To begin, consider a car moving with a constant, rightward (+) velocity - say of +10 m/s.
GRAPH IT!

10. POSITION-TIME GRAPHS

11. POSITION-TIME GRAPHS
• Now consider a car moving with a rightward (+), changing velocity - that is, a car that is moving
rightward but speeding up or accelerating.
• GRAPH IT!

12. POSITION-TIME GRAPHS

13. POSITION-TIME GRAPHS
• COMPARE
POSITIVE VELOCITY POSITIVE VELOCITY
CONSTANT VELOCITY CHANGING VELOCITY (ACCELERATION

14. POSITION-TIME GRAPHS
• What about SLOPE?
• "As the slope goes, so goes the velocity."
• Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa).
• If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing,
then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e.,
moving upwards and to the right).

15. POSITION-TIME GRAPHS
• Contrasting a Slow and a Fast Motion, Positive and Negative, ALL CONSTANT VELOCITY

16. POSITION-TIME GRAPHS
• Contrasting a Slow and a Fast Motion
Positive, Slow, Positive, Fast, Negative, Slow, Negative, Fast,
Constant Velocity Constant Velocity Constant Velocity Constant Velocity

17. POSITION-TIME GRAPHS
• Representing an Accelerated Motion
• Curved lines have changing slope – IN THIS CASE MEANS CHANGING VELOCITY a.k.a. ACCELERATION!!

18. POSITION-TIME GRAPHS
• Representing an Accelerated Motion
• Curved lines have changing slope – IN THIS CASE MEANS CHANGING VELOCITY a.k.a. ACCELERATION!!
NEGATIVE VELOCITY NEGATIVE VELOCITY
SLOW to FAST VELOCITY FAST TO SLOW VELOCITY
NEGATIVE ACCELERATION POSITIVE ACCELERATION

19. POSITION-TIME GRAPHS
• Constant Rightward Velocity
• Constant Leftward Velocity
• Rightward Velocity with a Rightward Acceleration
• Rightward Velocity with a Leftward Acceleration
• Leftward Velocity with a Leftward Acceleration
• Leftward Velocity with a Rightward Acceleration
• Passing Lane - Position vs. Time Graph

20. ACTIVITY
• Graph that Motion
• Graphs and Ramps

21. CHECK
• In your description, be sure to include such information as the direction of the velocity vector (i.e.,
positive or negative), whether there is a constant velocity or an acceleration, and whether the object is
moving slow, fast, from slow to fast or from fast to slow.

22. CHECK
Practice A Practice B
Positive, Changing Velocity Negative, Changing Velocity
Slow to Fast Slow to Fast
Positive Acceleration Negative Acceleration

23. POSITION-TIME GRAPHS
• The Meaning of Slope for a p-t Graph
• The slope of a position vs. time graph reveals pertinent information about an object's velocity.
• For example, a small slope means a small velocity; a negative slope means a negative velocity; a
constant slope (straight line) means a constant velocity; a changing slope (curved line) means a
changing velocity. Thus the shape of the line on the graph (straight, curving, steeply sloped, mildly
sloped, etc.) is descriptive of the object's motion.

24. • Determining the Slope on a p-t Graph

25. CHECK

26. CHECK
-3m/s

27. CHECK

28. CHECK
4m/s

29. VELOCITY – TIME GRAPH
• Constant Velocity versus Changing Velocity

30. VELOCITY – TIME GRAPH
• Constant Velocity versus Changing Velocity

31. VELOCITY – TIME GRAPH
• Constant Velocity versus Changing Velocity

32. VELOCITY – TIME GRAPH
• Constant Velocity versus Changing Velocity

33. VELOCITY – TIME GRAPH
• Constant Velocity versus Changing Velocity
POSITIVE VELOCITY POSITIVE VELOCITY
ZERO ACCELERATION POSITIVE ACCELERATION

34. • The principle is that the slope of the line on a velocity-time graph reveals useful information about the
acceleration of the object.
• If the acceleration is zero, then the slope is zero (i.e., a horizontal line).
• If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).
• If the acceleration is negative, then the slope is negative (i.e., a downward sloping line).

35. • Positive Velocity versus Negative Velocity
• a positive velocity means the object is moving in the positive direction; and a negative velocity means
the object is moving in the negative direction. So one knows an object is moving in the positive
direction if the line is located in the positive region of the graph (whether it is sloping up or sloping
down). And one knows that an object is moving in the negative direction if the line is located in the
negative region of the graph (whether it is sloping up or sloping down).

36. • Speeding Up versus Slowing Down
• Speeding up means that the magnitude (or numerical value) of the velocity is getting large. For
instance, an object with a velocity changing from +3 m/s to + 9 m/s is speeding up. Similarly, an object
with a velocity changing from -3 m/s to -9 m/s is also speeding up. In each case, the magnitude of the
velocity (the number itself, not the sign or direction) is increasing; the speed is getting bigger.

37. • Passing Lane - Velocity vs. Time Graph
• The Stoplight
• Motion of a Two-Stage Rocket

38. CHECK
• 1. Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that
are true):
• moving in the positive direction.
• moving with a constant velocity.
• moving with a negative velocity.
• slowing down.
• changing directions.
• speeding up.
• moving with a positive acceleration.
• moving with a constant acceleration.

39. CHECK
• 1. Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that
are true):
• Answers: a, d and h apply.
• a: TRUE since the line is in the positive region of the graph.
• b. FALSE since there is an acceleration (i.e., a changing velocity).
• c. FALSE since a negative velocity would be a line in the negative region (i.e., below the horizontal axis).
• d. TRUE since the line is approaching the 0-velocity level (the x-axis).
• e. FALSE since the line never crosses the axis.
• f. FALSE since the line is not moving away from x-axis.
• g. FALSE since the line has a negative or downward slope.
• h. TRUE since the line is straight (i.e, has a constant slope).