1. Position, Speed, and Velocity Ch. 4 Physical Science
Motion (in 1 –D)
Position, Speed, and Velocity
Ch. 4
Physical Science

2. MOTION
Motion is a change in the position of a body or system with respect to time.
Position is the location of a body or system at a given time.
Motion can be mapped by a coordinate system.
Coordinate Systems show the original location of the body (it’s initial or zero point) and the direction in which the body moves.
North, Up, (+)
West, Left,
Backward,(-)
East, Right,
Forward,(+)
South, Down, (-)

3. DISPLACEMENT vs. DISTANCE
Distance is the total length an object traveled.
It is a scalar quantity, which means it only has magnitude.
(Magnitude refers to the amount)
Displacement is the change in position of an object.
It is a vector quantity, which means it has magnitude & direction.
Objects at rest have a displacement of zero.
Displacement is NOT the same as the distance traveled.

4. Example: A man traveled from point A to B to C to D.
What is his displacement?
He is back in his original position.
A to B is 4m east
C to D is 4m west→ 0 m
they cancel each other out!
B to C is 2m south
D to A is 2m north → 0m
What is his distance?
4m + 2m + 4m + 2m = 12m

5. Equation for Displacement
∆d = df – di
d stands for position
f is for final position
i is for initial position
Draw a picture of the situation.
Set-up your problem using two-column format
List your equation & givens:
Substitute into equation and
Solve
∆d = df – di
df = 10 m
di = 5 m
∆d = ?
∆d = 10 m – 5 m
∆d= 5 m

6. Sample Problems
Example #1: If the starting position of an object is 50 m west and the final position is 150 m east, what is the displacement?
Example #2: If the starting position is 200 m north and the final position is 75 m south, what is the displacement?

7. VELOCITY
Velocity: the quantity that measures how fast something moves from one point to another
-or- How fast you can move in a specific direction.
Average Velocity: the total displacement divided by the time interval during which displacement occurred.
Instantaneous Velocity: The speed and direction of an object at a particular instance in time.

8. Speed Vs. Velocity Speed is a SCALAR quantity – it has only magnitude
Average speed is the distance traveled divided by the time interval.
Velocity is a VECTOR quantity
– it has magnitude & direction.
Average Velocity is the displacement of an object divided by the time interval.
SPEED
VELOCITY

9. Equations
VELOCITY
SPEED

10. Problem Solving RULES:
Draw a picture (motion diagram)
Two Column Format:
Left Side - Write the equation. Make a list of your given (with units) and unknown values.
Right Side - Substitute your numbers (with units) into the equation. Solve the problem, box in your final answer.

11. Velocity & Speed Practice
Joe and Sue take a 45 minute walk along a straight road to a store 3.0 km away. What is their average speed in km/hour?
A bus traveled on Newburg Road from a bus stop on 8 mile south to a stop at 5 mile in 15 minutes (lucky for the bus all of the lights were green!). What is the bus’s average velocity?
Simpson drives his car with an average velocity of 24 m/s toward the east. How long will it take him to drive 560 km on a perfectly straight highway?

12. MOTION Diagrams
A motion diagram (or map) represents the position, velocity, and acceleration of an object at various clock readings.
Arrows called vectors
are used to indicate the
direction and magnitude
of the object in motion. V V V V V

13. Motion Diagram
Describe the position, velocity, and acceleration shown by each motion diagram.
● ● ● ● ●
● ● ● ● ● ●
● ● ● ● ● ●
● ● ● ● ●

14. Velocity (speed) & P-T Graphs
You can determine the velocity of an object by finding the slope of position vs. time.
Slope = Rise (∆y axis)
Run (∆x axis)
Slope = 30 m – 10 m = 20 m = 10 m/s
3 s – 1 s s
Time
(s)
Position
(m) 1 10 2 20 3 30 4 40 5 50

15. 4.2 Position time graph
A position versus time graph shows a more detailed history of the drive, including
when the car was moving, and when it was stopped. The graph shows that during
the first hour, your position gradually increased from your initial position (0 miles)
to a point 60 miles away. It then shows that you were stopped between 1 hour and
1.5 hours because your position didn’t change. Finally, the graph shows that you
started driving again at 1.5 hours and changed your position until you reached a
point 90 miles away from your starting point. The graph contains much more
information because it shows the instantaneous speed all through the trip.

16. 4.2 Interpret a position time graph
The position versus time graph shows a boat traveling through a long canal.
The boat has to stop at locks for changes in water level.
a) How many stops does the boat make?
b) What is the boat’s average speed for the whole trip?
c) What is the highest speed the boat reaches?
A position versus time graph shows a more detailed history of the drive, including
when the car was moving, and when it was stopped. The graph shows that during
the first hour, your position gradually increased from your initial position (0 miles)
to a point 60 miles away. It then shows that you were stopped between 1 hour and
1.5 hours because your position didn’t change. Finally, the graph shows that you
started driving again at 1.5 hours and changed your position until you reached a
point 90 miles away from your starting point. The graph contains much more
information because it shows the instantaneous speed all through the trip.

17. Constant Speed
On this graph, a constant speed is a straight horizontal line.

20. Application: Slow-motion Photography
A video camera does not photograph moving images.
It takes a sequence of still images called frames and changes them fast enough that your brain perceives a moving image.
You can use an ordinary video camera to analyze motion in laboratory experiments.

21. Stop action photography is cool.
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22. Graphs -Position-time
Straight line = constant speed.
Slope tells velocity. (v = ∆d/∆t)
Positive slope is positive velocity (going forwards)
Negative slope is negative velocity (going backwards)
Horizontal line = zero slope = stopped
Change in slope means change in speed.

23. Graphs -Velocity-time
Horizontal line = constant speed (velocity)
Curved line = change in velocity (not constant)
Straight line (not horizontal) = constant change in velocity
Slope tells change in velocity
Positive slope = constant acceleration (speeding up)
Negative slope = constant acceleration (slowing down)
Area under curve = distance travelled
(v x t = d) m/s x s = m (when horizontal);
½ v x t =d (when sloped)
Instantaneous velocity is tangent to curve at any point.
Avg velocity is found between two points.

24. 4.3 Acceleration
If your speed increases by 1 meter per second (m/s) for each second, then your acceleration is 1 m/s per second.
Acceleration is the rate at which your speed (or velocity) changes.

25. 4.3 Acceleration
If the hill is steeper, the acceleration is greater.

26. 4.3 Acceleration
There is zero acceleration at constant speed because the speed does not change.

27. 4.3 Acceleration Speed and acceleration are not the same thing.
You can be moving (non-zero speed) and have no acceleration (think cruise control).
You can also be accelerating and not moving!
A falling object begins accelerating the instant it is released.

28. 4.3 Acceleration Acceleration describes how quickly speed changes.
Acceleration is the change in speed divided by the change in time.

29. 4.3 Acceleration on motion graphs
The word “acceleration” is used for any change in speed, up or down.
Acceleration can be positive or negative.

30. 4.3 Acceleration on speed-time graphs
Positive acceleration adds more speed each second.
Things get faster.
Speed increases over time.

31. 4.3 Acceleration on speed-time graphs
Negative acceleration subtracts some speed each second.
Things get slower.
People sometimes use the word deceleration to describe slowing down.

32. 4.3 Acceleration on position-time graphs
The position vs. time graph is a curve when there is acceleration.
The car covers more distance each second, so the position vs. time graph gets steeper each second.

33. 4.3 Acceleration on position-time graphs
When a car is slowing down, the speed decreases so the car covers less distance each second.
The position vs. time graph gets shallower with time.

35. 4.3 Free fall
An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it.

36. 4.3 Free fall The letter “g” is used for acceleration due to gravity.
Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2
The letter “g” is used for acceleration due to gravity.

37. 4.3 Acceleration and direction
Acceleration occurs whenever there is a change in speed, direction, or both.

38. 4.3 Acceleration and direction
A car driving around a curve at a constant speed is accelerating because its direction is changing.

40. 4.3 Curved motion Circular motion is another type of curved motion.
An object in circular motion has a velocity vector that constantly changes direction.