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?