Section 2.4 Graphs of Motion. Why Use Graphs? Show relationships between distance, velocity, acceleration, and time Visual and clear way of representing.

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Presentation transcript:

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 Graphs Constant Speed What information can we get from this graph?

Position vs. Time Graphs Constant 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 a Position 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 a Position 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 Graphs Accelerated 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 Graphs Accelerated Motion

Speed vs. Time Graphs Constant 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 Graphs Accelerated 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 Graphs Accelerated 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 Graphs Accelerated 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/s 2

Speed vs. Time Graphs Accelerated 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?