1. Motion
Position, Speed and Velocity
Graphs of Motion
Acceleration

2. Learning Goals Explain the meaning of motion.
Describe an object’s position relative to a reference point.
Use the speed formula.
Tell the difference between speed and velocity.

3. Position, Speed and Velocity
Position is a variable given relative to an origin.
The origin is the place where position equals 0.
The position of this car at 50 cm describes where the car is relative to the track.

4. Position, Speed and Velocity
Position and distance are similar but not the same.
If the car moves a distance of 20 cm to the right, its new position will be 70 cm from its origin.
Distance = 20 cm
New position

5. Position, Speed and Velocity
The variable speed describes how quickly something moves.
To calculate the speed of a moving object divide the distance it moves by the time it takes to move.

7. Position, Speed and Velocity
The units for speed are distance units over time units.
This table shows different units commonly used for speed.

8. Average speed
When you divide the total distance of a trip by the time taken you get the average speed.
On this driving trip around Chicago, the car traveled and average of 100 km/h.

9. Instantaneous speed A speedometer shows a car’s instantaneous speed.
The instantaneous speed is the actual speed an object has at any moment.

10. Solving Problems
How far do you go if you drive for two hours at a speed of 100 km/h?
Looking for:
…distance
Given:
…speed = 100 km/h time = 2 h
Relationships:
d = vt
Solution:
d = 100 km/h x 2 h = 200 km
= 200 km

11. Vectors and velocity Position uses positive and negative numbers.
Positive numbers are for positions to the right of the origin and negative numbers are for positions to the left the origin.

12. Vectors and velocity
Distance is either zero or a positive value.

13. Vectors and velocity
We use the term velocity to mean speed with direction.

15. Solving Problems
A train travels at 100 km/h heading east to reach a town in 4 hours. The train then reverses and heads west at 50 km/h for 4 hours. What is the train’s position now?
Looking for:
…train’s new position
Given:
…velocity = km/h, east ; time = 4 h
…velocity = km/h, west ; time = 4 h
Relationships:
change in position = velocity × time

16. Solution: Solving Problems 1st change in position:
(+100 km/h) × (4 h) = +400 km
2nd change in position:
(−50 km/h) × (4 h) = −200 km
Final position:
(+400 km) + (−200 km) = +200 km
The train is 200 km east of where it started.

17. How is motion described and measured in physics?
Investigation
Time, Distance & Speed
Key Question:
How is motion described and measured in physics?

18. Learning Goals
Construct and analyze graphs of position versus time, and speed versus time.
Recognize and explain how the slope of a line describes the motion of an object.
Explain the meaning of constant speed.

19. Graphs of Motion Constant speed means the speed stays the same.
An object moving at a constant speed always creates a position vs. time graph that is a straight line.

20. Graphs of Motion
The data shows the runner took 10 seconds to run each 50-meter segment.
Because the time was the same for each segment, you know the speed was the same for each segment.

24. Graphs of Motion
You can use position vs. time graphs to compare the motion of different objects.
The steeper line on a position vs. time graph means a faster speed.

25. Slope The slope of a line is the ratio of the “rise” to the “run”.
The steepness of a line is measured by finding its slope.

27. Graphs of changing motion
Objects rarely move at the same speed for a long period of time.
A speed vs. time graph is also useful for showing the motion of an object that is speeding up or slowing down.

28. Graphs of changing motion
On the graph, the length is equal to the time and the height is equal to the speed.
Suppose we draw a rectangle on the speed vs. time graph between the x-axis and the line showing the speed.
The area of the rectangle is equal to its length times its height.

31. Learning Goals Define acceleration.
Determine acceleration by mathematical and graphical means.
Explain the role of acceleration in describing curved motion and objects in free fall.

32. Investigation
Acceleration
Key Question:
What is acceleration?

33. 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.

34. Acceleration Acceleration is easy to spot on a speed vs. time graph.
Acceleration causes the line to slope up on a speed vs. time graph.
Acceleration is easy to spot on a speed vs. time graph.
What is the bike’s acceleration?

35. Acceleration
If the hill is steeper, the acceleration is greater.

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

37. 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.

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

40. Speed and acceleration
An acceleration of 20 km/h/s means that the speed increases by 20 km/h each second.
The units for time in acceleration are often expressed as “seconds squared” and written as s2.
Can you convert this rate using conversion factors?

41. A strong wind increases its speed to 4 m/s in 3 s.
Solving Problems
A sailboat moves at 1 m/s.
A strong wind increases its speed to 4 m/s in 3 s.
Calculate acceleration.

42. = 1 m/s2 Solving Problems Looking for: …acceleration of sailboat
Given:
…v1 = 1 m/s; v2 = 4 m/s; time = 3 s
Relationships:
a = v2 – v1/t
Solution:
a = (4 m/s – 1 m/s)/ 3 s
= 1 m/s2

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

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

45. 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.

46. 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.

47. 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.

49. 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.

51. 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

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

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

55. Acceleration and direction
Individual vectors can be drawn to scale to calculate the change in direction.

56. Curved motion A soccer ball is an example of a projectile.
A projectile is an object moving under the influence of only gravity.
The path of the ball makes a bowl-shaped curve called a parabola.

57. Studying Two Part Motion
Investigation
Studying Two Part Motion
Key Question:
What happens to the Energy Car as it travels down a hill and across a flat section of track?