Lesson 6 Velocity vs. Speed

  Area under Speed-Time Graphs

What can the area under a speed-time graph tell us about an object’s motion?

We have learned how to use position-time graphs to interpret an object’s speed, and also learned about speed-time graphs. Graphs are particularly useful as well because we can determine the distance an object travels. We can do this by finding the area under the curve of a speed-time graph.

Determining the Area under a Speed-Time Graph

Finding the area under the line of a speed-time graph is an important skill that is used in science to help understand more about an object’s motion.

Mathematically, remember to determine the area of a rectangle, the formula is:

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and to determine the area of a triangle, the formula is:

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For example, image C6.23 is a graph of a hummingbird travelling at a uniform velocity of 12 m/s [E] for 5.0 s.

If the area under a velocity-time graph is determined, then what value are you finding?

 If a hummingbird travels at a uniform velocity of 12 m/s [E] for 3.5 s, what is its displacement?

You can determine the area under the graph.

A = b × h = time(s) × velocity (m/s)
A = (3.5 s)(12.0 m/s [E]) = 42 m [E]
 
So, the area under a velocity-time graph is a measurement of displacement.

For example, image C6.25 is a graph of a car travelling [N] that is steadily increasing its velocity.

If the car steadily increases its velocity for 4.0 s, what is its displacement?

You can determine the area under the graph.

The base (x-axis) is 4.0 s. The height (y-axis) is 12.0 m/s [N].

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  Read This

Please read pages 144 and 477 in your Science 10 textbook. Make sure you take notes on your readings to study from later. You should focus on how to calculate the area under a velocity-time graph, and the information that can be interpreted from the area under a velocity-time graph. Remember, if you have any questions, or do not understand something, ask your teacher!

  Practice Questions

Complete the following practice questions to check your understanding of the concept you just learned. Make sure you write complete answers to the practice questions in your notes. After you have checked your answers, make corrections to your responses (where necessary) to study from.

1. Explain how the area under a velocity-time graph is useful in explaining an object’s motion.
   
   
   Check your work.
   

   Your answer should be a variation of the following.
   The area under a velocity-time graph shows the displacement of a moving object.
2. In Image C6.25 in Lesson 6, a graph of a car travelling [N] was provided.
   
   
   
   

   

   C6.25 Velocity-Time Graph

   
   
   
   If the car steadily increases its velocity for 2.0 s to 5.0 s, what is its displacement in this time period?
   
   
   Check your work.
   

   You can determine the area under the graph.
   The base (x-axis) is 3.0 s (5.0 s – 2.0 s). The height (y-axis) is 9.0 m/s [N] (15.0 – 6.0)
   
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