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


21 Responses to “Constant Acceleration”
  1. Aurora says:

    You can just use the PDF file worksheet – it’s about the some. The main difference is that in the xls spreadsheet, I’ve already pt in the equations with sample data. If you really want to look at it, try a friend’s computer?

    I know Google Sheets is popular now, but it simply isn’t powerful enough for most scientists and engineers to use when they start plotting their data and doing graphs and statistical analysis.

  2. michelle_s says:

    I do not have the excel program to open or print off some of the printouts. Is there another way?

  3. Aurora says:

    Hi there,

    I’ve sent you a private email that has additional information that I hope is helpful. Let me know if you didn’t get it.


  4. jackson119 says:

    We are having a lot of difficulty figuring this program out. We’ve done the driveway races but can’t figure out the worksheet. Our average distances were 18″ at 1 sec, 45″ at 2 sec and 106″ at 3 sec. We graphed those. Then it says to square the time and take half of it so we got .5 sec, 2 sec. and 4.5 sec. What do you mean by “what is left will be your acceleration?” How do we graph the results of our modified time? How are we supposed to know the distances of those times? And the second question in the following exercises part says to calculate the slope of the line but doesn’t explain how. Also, there was a link to “Student worksheet and exercises” and then it said advanced students should download “Driveway Races Lab” What is meant by advanced students? Is that for AP physics? Is this course all AP? I feel like we are so lost already and we’re just in the intro lesson. Was there a prerequisite class that we needed before this one? Please help!

  5. Aurora says:

    Oh, no! I am so sorry you’re still struggling. I’ve sent you a private email with images and links in it so you can clearly see where to click and find what you need. I hope this is helpful, and let me know if you still need help. As for your question about rounding – we’re not rounding, but rather using “significant digits” to get our answer. There’s complete instructions on how to do this here: and here:

  6. nancy_axel says:

    Thanks Aurora but we are still struggling. When we work out the problem we get 666,666m/s².
    Are you rounding?

    Also, I have searched everywhere and don’t see complete explanations of you working out the answers to the physics problems. Your link just takes me to the first page of the Advanced Physics class. I don’t see anything there that we didn’t already watch. My son has watched all the videos on each lesson page up through the Pop Rockets page and is getting more and more lost. The activities at the end of that lesson are almost impossible for us to work out. (For example: even if we use your diagram and example problem at the bottom of page 3 of the Pop Rockets Activity pages we are trying to see how you are using the formula there but it’s not making sense to me. it appears you have plugged 1.3 sec in for the time but in the problem you said it took 1.2 sec. That’s confusing. And I don’t know how to get the (-9.8m/s²) that you used for the acceleration. We must be missing something.
    I see that at the end of the unit there is a Worksheet for 1-D Kinematics that has answers written out but I couldn’t find any of those problems that would have helped us solve bullet acceleration problem above. It may be that we need to just pull back and do the 8th grade physics first. However I’m not sure that is going to help us once we pick back up here and try doing this math.

  7. Aurora says:

    Sorry I didn’t see this question last week – my apologies for the delay. We’re still getting setup for the school year here – so busy!

    I am concerned you aren’t in the right section of the program. I do have complete explanations of me working out physics problems for most of the program in Advanced Physics, and all the homework have full solutions, not just answers. Did you find those yet? They start here:

    That way you don’t have to worry about “how do I solve this?” There’s about 550 videos just in the physics section alone that detail all the different sorts of problems you’re going to encounter in physics.

    Ok now onto your question – it seems like a math problem – you’re so close to the answer! All you need to do is solve the equation for “a” like this:

    d = (0.5) a (t^2)
    d / (0.5) = a (t^2)

    We can flip the 1/2 on the bottom so it looks like this:

    2d = a (t^2)

    Now solve for a:

    2d/(t^2) = a

    So you punch into a calculator: 2 x (0.75) and then divide it by (0.0015 x 0.0015) to get 666,000 m/s^2.

    Let me know if you need more help. And make sure you’ve seen the step by step instructional videos that have details on how to solve these types of problems.

  8. nancy_axel says:

    Acceleration problem from #3 on worksheet Unit 2 Lesson 2 :

    When a bullet is fired from a rifle it accelerates from a velocity of 0m/s to top speed in a distance of .75m in a time of .0015s. What is the acceleration experienced by the bullet?

    Would you please show us the math for how to work this problem out using d=1.2at²?

  9. nancy_axel says:

    Oops. I meant a velocity of 0 m/s not 9 m/s. Sorry for the typo!

  10. nancy_axel says:

    Thanks for answering our question so quickly!
    But apparently I didn’t communicate well. I know this is posted under the driveway races experiment but I wasn’t sure where to post our question. We were dealing with an acceleration problem so I just picked a teaching page about acceleration.
    We are working on the acceleration problems at the end of Unit 2. Lesson 2. On your worksheet problem number 3 asks:

    When a bullet is fired from a rifle it accelerates from a velocity of 9m/s to top speed in a distance of /75m in a time of .0015s. What is the acceleration experienced by the bullet?

    So using the formula: d=1/2at²
    our equation looks like this:

    We are simply needing help with the math involved to get that to equal your answer: 666,000m/s²
    The closest we could get was: 681,816 m/s²

    I’m not good at math and know zero physics so we may end up needing too much help with this program since your answer keys just have answers and no explanations or show any work.

  11. Aurora says:

    Let’s take a look. For your equation, it should look like this:

    (distance) = 1/2 (acceleration) x (time)^2

    There aren’t any units in the one you posted, so I am not sure of what the value are that you inserted in your example. I am guessing you meant to put in 0.75 meters for distance and 0.0015 seconds (how did you measure something that small?) If so, your ball went far (nearly a meter) in a very, very short amount of time (1.5 milliseconds). So the acceleration number you calculated looks about right. I am thinking you’ll want to recheck the numbers you put in and try again?

  12. nancy_axel says:

    We are working out the acceleration problems for Unit 2 and are getting stuck on number 3.
    When we plug in the distance and time we get an equation that looks like this:

    .75= 1/2 a (.0015) ²

    Is this correct? When we solve from here we don’t get your answer: 666,000m/s²

    If our equation is correct maybe you could explain how to work out the math from there.
    Thanks, Nancy

  13. cndbil says:

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

  14. 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:

  15. 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

  16. Aurora says:

    Thanks for the update!

  17. Kimberly Voelkel says:

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

  18. Aurora says:

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

  19. 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. 🙂

  20. 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!

  21. 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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