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Section 2.4
Graphs of Motion
Why Use Graphs?
Show relationships between distance, velocity, acceleration, and time
Visual and clear way of representing data
What are some examples of graphs you see everyday?
Position vs. Time GraphsConstant Speed
What information can we get from this graph?
Position vs. Time GraphsConstant Speed
What information can we get from this graph? Distance traveled Time it took We can see that car
A was faster, but we can also calculate the speed from the graph alone!
Calculating Speed from aPosition vs. Time Graph
We can calculate the speed by finding the slope of the line in a position vs. time graph
Slope = the “rise” (vertical change) to the “run” (horizontal change)
Calculating Speed from aPosition vs. Time Graph
This makes sense because the rise is position (distance) and the run is the time
Remember, speed is calculated by dividing distance by time (which is what we are doing when we find slope)
How to Calculate Slope
Find the height, which is the distance traveled
Find the length, which is the time it took
Divide and solve For a position vs.
time graph, the slope tells us the speed
Position vs. Time GraphsAccelerated Motion
Position vs. Time graphs have a different graph depending on if the object is accelerating or traveling at a constant speed (not accelerating)
Constant speed (not accelerating) = line
Increasing/Decreasing speed (accelerating) = curve
Position vs. Time GraphsAccelerated Motion
Speed vs. Time GraphsConstant Speed
Speed vs. Time GraphsConstant Speed
How to find the distance traveled with a speed vs. time graph: Find the area under the line
A = l x w
(length x width) …for a rectangle
Speed vs. Time GraphsAccelerated Motion
If an object is accelerating, it is easier to work with the speed vs. time graph instead of the position vs. time graph because it clearly shows how an object’s speed changes with time
Speed vs. Time GraphsAccelerated Motion
Remember
The slope of a position vs. time graph gave us the speed
The slope of a speed vs. time graph gives the acceleration
Speed vs. Time GraphsAccelerated Motion
We calculate slope the same as before—rise over run
Question
Calculate the acceleration from the graph
Question
Calculate the acceleration from the graph
a = 4 m/s2
Speed vs. Time GraphsAccelerated Motion
Distance is found the same way, too
Find the area under the line!
A = ½ b x h
(base x height) …for a triangle
Section 2.4 Review
1. Explain how to calculate the slope of a graph.
2. What does the slope of a position versus time graph represent?
Section 2.4 Review
3. Draw the position versus time graph and the speed versus time graph for an object moving at a constant speed of 2 m/sec.
4. How can you use a speed versus time graph to find an object’s acceleration?