1. Distance-Time Graphs

2. Review - Speed v=d/t Speed:
The measure of how fast/slow something moves a particular distance over a given amount of time.
It can then be calculated using the following formula:
v=d/t

3. How do you graph speed? Graphs are always set up the same way:
Y - axis
X- axis

4. Distance - Time Graphs
On a distance time graph, the distance will always be the dependent variable on the y- axis.
Time is the independent variable and will always be placed on the x-axis.
Y - axis
X- axis

5. Lines on the Graphs
The lines on the graphs can tell you many different things. For example:
The slope of a line (steepness) can tell you speed.
If the slope is steep (more vertical) then the speed is fast.
If the slope is flatter (more horizontal) then the speed is slow.
If the line is completely flat or horizontal then the object has no speed or is stopped.

6. Examples of distance-time graphs
FAST
STOPPED
SLOW

7. Other things we can learn from a graph:
We can also show the direction the object is traveling. The point on the graph where the x and y axis meet is the reference point or where the object’s home base is located (their starting point).
If the arrow or line is pointing away or moving away from the x axis then the object is moving away from their reference point or starting point.
If the arrow or line is pointing toward or moving toward the x axis then the object is moving back to the reference point.

8. Leaving and coming back:

9. Speeding up and Slowing down
The object is speeding up and has positive acceleration.
The object is slowing down and has negative acceleration.

10. Practice reading graphs

11. Determining Speed from a graph
V=d/t
Think of the graph in sections divided by each line segment
Then determine the total distance for the line segment you are looking at.
Then determine the total time for that segment.
Finally, use the equation to determine speed of the line segment.
Example: the object traveled a total distance of 25 m for the first segment. It took the object 20 seconds. v=d/t v=25/20 v= 1.25 m/s

12. Practice Calculate the speed for last line segment:
Distance traveled = 25 m
Time = 10 sec
v=d/t 25/10
2.50 m/sec
Was the object moving faster or slower than when they started?

13. Practice on your own: Calculate the speed for the first segment.
Calculate the speed for the third segment.

14. Graphs and Stories
This object left the reference point at a fast constant pace.
They then stopped for a brief period of time.
Finally they began to move again but at a slower rate.

15. Example with stories
Joe left home at a moderate constant speed. He realized that he forgot his wallet and turned around to go home to get it. However, while walking back he realized it was in his pocket so he turned around to head back to his friend’s house. He picked up his pace a little to help make up some lost time. When he got to his friend’s house they stayed to watch a movie.

16. You Practice writing a story
Distance (m)