Graphing Motion

1
Graphing Motion

2
Graphs

• Graphs can show how objects change position or
  speed. (How far away was the turtle after 60
  seconds?)

3
Position-Time Graphs

• Graphs often show how something changes with
  time.
• This graph shows how temperature changes with
  time in Santa Barbara, California.

4
Making a Position-Time Graph

• This table shows how far a turtle has moved after
  an amount of time.

5
Making a Position-Time Graph (cont.)

• Plotting the time on the x-axis and plotting the
  distance the turtle has moved on the y-axis
  creates the graph.
• You can draw a line through the points and use it
  to estimate the turtles position at a given
  time. (Estimate the position of the turtle at 90
  seconds)

6
Units on Position-Time Graphs

• Each number has units associated with it.
• Position has units of length like cm, m, or km.
• Seconds, minutes, and days are units of time.

7
Slope of a Position-Time Graph

• The steepness of a line on a graph is called the
  slope.
• The steeper the slope, the faster the object is
  traveling. (Which line represents a faster moving
  turtle?)
• On a position-time graph, a steeper line means a
  greater average speed.

8
Calculating Slope from a Position-Time Graph

• To find the slope of a line, the origin and
  another point are used to calculate the rise and
  the run.

9
Calculating Slope from a Position-Time Graph
(cont.)

• Rise is the change in vertical direction (up and
  down).
• Run is the change in horizontal direction (left
  to right).

10
Slope and Average Speed

• Average speed is the total distance divided by
  the total time taken to travel that distance.
• Rise is equal to the distance traveled.
• Run is equal to the time taken to travel that
  distance.
• Average speed is equal to the slope of the line
  on a position-time graph.

11
Position-Time Graphs for Changing Speed

• Only objects with a constant speed will have
  position-time graphs with a straight line.

12
Position-Time Graphs for Changing Speed (cont.)

• To find the average speed of the entire trip, use
  the starting and ending points.

13
Position-Time Graphs for Changing Speed (cont.)

• Then calculate the slope of the line that would
  connect those points. (Calculate the slope using
  (0,0) and (10,10))

14
Speed-Time Graphs

• Graphing instantaneous speed of an object shows
  how the speed of an object changes with time.
• Constant speed on a speed-time graph is a
  horizontal line because the speed does not
  change.

15
Speed-Time Graphs (cont.)

• If an object speeds up, the plotted line slants
  up towards the right.

16
Speed-Time Graphs (cont.)

• If an object slows down, the plotted line slants
  down towards the right.

17
Speed-Time Graphs (cont.)
18
Lesson 1-3 Review

• The horizontal change on a graph is also called
  the ____.
• A rise
• B elevation
• C run
• D distance

19
Lesson 1-3 Review

• The steepness of a line on a graph is called the
  ____.
• A slope
• B hill
• C rise
• D run

20
Lesson 1-3 Review

• If the rise is equal to 75 m and the run is equal
  to 2.5 m, then what is the slope?
• A 187.5 m
• B 12 m
• C 30 m
• D 0.03 cm