Constant Acceleration

If something has an acceleration of 5 ft/s² how fast will it be going after 1 second…2 second…3 seconds? After one second it will be going 5 ft/s; after two seconds 10 ft/s; and after three seconds 15 ft/s. Again, it’s just like v = gt (v is velocity, g is the gravitational constant, t is time) but put the rate of acceleration of the object in place of g to get the formula v = at or velocity equals acceleration times time.

Once in a while, an object will change its velocity by the same amount at the same rate, and when this happens, it’s called constant acceleration, since the velocity is changing by the same amount each time. Note that constant acceleration is not the same as constant velocity. If an object is changing speed, no matter how consistently it does it, it’s still accelerating since it doesn’t have a constant velocity. Objects in free fall motion, like a sky diver, experiences constant acceleration and may also eventually reach a constant velocity, but this is a very special case (we’ll talk more about that later).

Average acceleration is found by dividing the average velocity (the difference between the initial and final velocity points) by the time lapsed between the two points. Acceleration is measured in a variety of units, but the most common are “meters per second squared” (m/s2) or “feet per second squared” (ft/s2).

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Download Student Worksheet & Exercises

Take a look at your marks. See how they get farther and farther apart as the ball continues to accelerate? Your ball was constantly increasing speed and as such, it was constantly accelerating. By the way, would it have mattered what the mass of the ball was that you used? No. Gravity accelerates all things equally. This fact is what Galileo was proving when he did this experiment. The the weight of the ball doesn’t matter but the size of the ball might. If you used a small ball and a large ball you would probably see differences due to friction and rotational inertia. The bigger the ball, the more slowly it begins rolling. The mass of the ball, however, does not matter.


  1. Was the line a straight line?
  2. It should be close now, and the slope represents the acceleration it experienced going down the ramp. Calculate the slope of this line.
  3. What do you think would happen if you increased the height of the ramp?
  4. Knowing what you do about gravity, what is the highest acceleration it can reach?

For Advanced Students…

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Is acceleration a scalar or a vector quantity? You could argue that it’s both actually, but in physics it’s usually a vector. This means that acceleration has a magnitude and a direction. The direction is either “+” or “-“, depending on if an object is increasing or decreasing speed. Usually, objects that speed up have their acceleration vector in the same direction as the object is moving in. If it’s slowing down, then the arrow flips to be in the opposite direction.

Click here to go to next lesson on Vector Diagrams


9 Responses to “Constant Acceleration”
  1. cndbil says:

    Thank you. I see it now. Yes we are doing the HS side

  2. Aurora says:

    That lesson is posted in two places. I noticed you’ve accessed it from the HS side, so the answers to the questions in the worksheet download are on the last page.

    If you meant to access it from the K-8 side, the answers to the questions are here:

  3. cndbil says:

    Hello. I have the same question Kimberly did. I cannot seem to find the solutions to the Acceleration problems. Please tell me where to look. Thank you

  4. Aurora says:

    Thanks for the update!

  5. Kimberly Voelkel says:

    We found the solutions to our question “A dog begins running and accelerates…”! Sorry about the confusion…..we got it now! 🙂

  6. Aurora says:

    Oh gosh, you’re right – these are missing! I’ll get these fixed and post the updated file right away.

  7. Kimberly Voelkel says:

    We have printed out the chapter 1 kinematics lesson. We did the driveway races and are answering questions provided with the lab. Is there an example page we could see to make sure we are doing this work properly? Also, there are acceleration problems included …”a dog begins running and accelerates at 2.5 m/s….” Where are the answers to these problems? Thank you for your help. We are learning and definitely need it. 🙂

  8. Aurora says:

    Let me see if I can help. The hands on build-it experiment labs are inter-mixed with the sit-down-with-a-sheet-of-paper videos as appropriate. The first lesson in 1D Kinematics is here:

    and at the bottom is a link that says “Click here to go to next lesson on Scalars and Vectors.” When you click on it, it takes you to the next lesson here:

    Below that video is the next one and so on. You go in sequence, and click on the next lab/lesson when you’re ready below the videos.

    If you want to see ALL the lessons and labs for a section, then you’d pick a link on the upper right (like “Describing Motion with Diagrams” for example).

    I apologize for the confusion with navigation. I am actually working on that right now to make it easier to know where you are and what’s next. Look for improvements soon!

  9. Susanne Evans says:

    My son did the lessons in 1-D Kinematics, section 1. I thought there would be labs associated with each lesson. I didn’t see any. There is one video showing at the end of the lessons, which, if we click it, it takes us to a page with a long list of experiments. These experiments don’t appear to be attached to any specific lesson. Do we have to hunt through them to see which one matches the lesson? Is the Physics unit not ready yet? Is there another advanced (High School) topic that has already been correlated with the lab work?


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