1. Physics and Graphs

2. graphs serve as pictures of mathematical relationships
because physics suggests that the universe behaves according to a set of mathematical relationships, graphs should also serve as pictures of physics relationships
we will be creating three different kinds of graphs in this section of the course:
1. distance – time graphs (d – t graphs) - these graphs are also called position – time graphs
2. velocity – time graphs (v – t graphs)
3. acceleration – time graphs (a – t graphs)

3. Position-Time Graphs
these graphs show the position of an object as time ticks by
time is plotted as the independent variable (x – axis)
distance or position is plotted as the dependent variable (y – axis)
Important Features:
the slope of the line on a d – t graphs represents an objects velocity

4. Velocity-Time Graphs
these graphs show the velocity of an object as time ticks by
time is plotted as the independent variable (x – axis)
velocity is plotted as the dependent variable (y – axis)
Important Features:
the slope of the line on a v – t graph represents an objects acceleration
the area under the line represents an objects position

5. Acceleration-Time Graphs
these graphs show the acceleration of an object as time ticks by
time is plotted as the independent variable (x – axis)
acceleration is plotted as the dependent variable (y – axis)
Important Features:
the area under the line represents an objects velocity

6. we must be able to use the information contained in any one of the three motion graphs to create the other two

7. Examples:
1. A bird flies at a rate of 10 ms-1 for 5 seconds. Create the corresponding d – t, v – t and a – t graphs.
2. A car accelerates from rest at a rate of 5.0ms-2 for 5 seconds. Create the corresponding d – t, v – t and a – t graphs.

8. when considering more complicated scenarios, we will often generate more complicated graphs
in situations like this, it is often easier to consider these graphs as being made up of various sections
build these graphs in pieces!
analyze these graphs in pieces!

9. Example:
A cat is sitting under a tree when it sees a bird across a large yard. The cat accelerates at a rate of 2.0 ms-2 for 4 seconds in hopes of catching lunch. The bird however, sees the cat coming and flies out of the cats reach. The cat continues to chase the bird while running at a top speed of 8.0 ms-1 for another 4 seconds before running into a fence.
Draw the d-t, v-t and a-t graphs that summarize this scenario. Be sure to include a data chart for each of the graphs!