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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This experiment is one of my favorites in this acceleration series, because it clearly shows you what acceleration looks like.
The materials you need is are:
Grab a friend to help you out with this experiment - it's a lot easier with two people.
Are you ready to get started really discovering what acceleration is all about?
Here's what you do:
1. Place the board on the books or whatever you use to make the board a slight ramp. You really don’t want it to be slanted very high. Only an inch or less would be fine. If you wish, you can increase the slant later just to play with it.
2. Put a line across the board where you will always start the ball. Some folks call this the “starting line.”
3. Start the timer and let the ball go from the starting line at the same exact time.
4. Now, this is the tricky part. When the timer hits one second, mark where the ball is at that point. Do this several times. It takes a while to get the hang of this. I find it easiest to have another person do the timing while I follow the ball with my finger. When the person says to stop, I stop my finger and mark the board at that point.
5. Do the exact same thing but this time, instead of marking the place where the ball is at one second, mark where it is at the end of two seconds.
6. Do it again but this time mark it at 3 seconds.
7. Continue marking until you run out of board or driveway.
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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.
Exercises
Let’s say for example that my ball went 6 inches in that first second. Dust off those old formulas and lets play with d=1/2gt² where d is distance, g is acceleration due to gravity and t is time.
We can’t use g here because the object is not in free fall, so instead of g let’s call it “a” for acceleration. Gravity is the force pulling on our ball but due to the slope, the ball is falling at some acceleration less then 32 ft/s².
In this case, d is 6 inches, t is 1 second and a is our unknown.
With a little math we see:
a = 12in/sec² (So our acceleration for our ramp is 12 in/sec² or we could say 1ft/s².)
With a little more math we can see how far our ball should have traveled for each time trial that we did. For one second we see that our ball should have traveled d=1/2 12(12) or d= 6 inches (we knew that one already didn’t we?).
For two seconds we can expect to see that d=1/2 12(22) or d=24 inches. For three seconds we expect d=1/2 12(32) or d= 54 inches.
Do you see why we need a pretty long board for this?
Now roll the ball down the ramp and actually measure the distance it travels after two and three seconds. Do your calculations match your results? Probably not. Our nasty little friend friction has a sneaky way of messing up results. You should definitely see the distance the ball travels get greater with each second however. So make yourself a table or use one of ours to record your data and jot down your calculations and chart your results like a real scientist.
Advanced students: Download your Driveway Races Lab here.
[/am4show] 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.
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).
[am4show have='p9;p58;' guest_error='Guest error message' user_error='User error message' ]
This experiment is one of my favorites in this acceleration series, because it clearly shows you what acceleration looks like.
The materials you need is are:
- a hard, smooth ball (a golf ball, racket ball, pool ball, soccer ball, etc.)
- tape or chalk
- a slightly sloping driveway (you can also use a board for a ramp that's propped up on one end)
Grab a friend to help you out with this experiment - it's a lot easier with two people.
Are you ready to get started really discovering what acceleration is all about?
Here's what you do:
1. Place the board on the books or whatever you use to make the board a slight ramp. You really don’t want it to be slanted very high. Only an inch or less would be fine. If you wish, you can increase the slant later just to play with it.
2. Put a line across the board where you will always start the ball. Some folks call this the “starting line.”
3. Start the timer and let the ball go from the starting line at the same exact time.
4. Now, this is the tricky part. When the timer hits one second, mark where the ball is at that point. Do this several times. It takes a while to get the hang of this. I find it easiest to have another person do the timing while I follow the ball with my finger. When the person says to stop, I stop my finger and mark the board at that point.
5. Do the exact same thing but this time, instead of marking the place where the ball is at one second, mark where it is at the end of two seconds.
6. Do it again but this time mark it at 3 seconds.
7. Continue marking until you run out of board or driveway.
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.
Exercises
- Was the line a straight line?
- It should be close now, and the slope represents the acceleration it experienced going down the ramp. Calculate the slope of this line.
- What do you think would happen if you increased the height of the ramp?
- Knowing what you do about gravity, what is the highest acceleration it can reach?
For Advanced Students...
[am4show have='p9;p39;' guest_error='Guest error message' user_error='User error message' ] Now if you want to whip out your calculators you can find out how fast your ball was accelerating. Take your measuring tape and measure the distance from the starting line to the line you made for the distance the ball traveled in one second.Let’s say for example that my ball went 6 inches in that first second. Dust off those old formulas and lets play with d=1/2gt² where d is distance, g is acceleration due to gravity and t is time.
We can’t use g here because the object is not in free fall, so instead of g let’s call it “a” for acceleration. Gravity is the force pulling on our ball but due to the slope, the ball is falling at some acceleration less then 32 ft/s².
In this case, d is 6 inches, t is 1 second and a is our unknown.
With a little math we see:
a = 12in/sec² (So our acceleration for our ramp is 12 in/sec² or we could say 1ft/s².)
With a little more math we can see how far our ball should have traveled for each time trial that we did. For one second we see that our ball should have traveled d=1/2 12(12) or d= 6 inches (we knew that one already didn’t we?).
For two seconds we can expect to see that d=1/2 12(22) or d=24 inches. For three seconds we expect d=1/2 12(32) or d= 54 inches.
Do you see why we need a pretty long board for this?
Now roll the ball down the ramp and actually measure the distance it travels after two and three seconds. Do your calculations match your results? Probably not. Our nasty little friend friction has a sneaky way of messing up results. You should definitely see the distance the ball travels get greater with each second however. So make yourself a table or use one of ours to record your data and jot down your calculations and chart your results like a real scientist.
Advanced students: Download your Driveway Races Lab here.
[/am4show] 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.
It is best to do this experiment with a ball. But after that, feel free to try it with anything that rolls…even a Hot Wheels car. But Hot Wheels roll best inside a track and that would be a pretty long track!
can i use a hot wheels car?
Feel free to try a marble. But, a marble is usually to small. It will often bounce due to small imperfections in the surface and it will be affected by cracks in the pavement.
Yes, it’s pretty neat!
and can I use a marble?
have you ever seen GEO-FS flight sim ?
Yes, posting a comment is a good first step. But since you are working on a specific problem, it will be best to send me an email. Please take a picture of your work and email it to [email protected]. Please share a reminder in the email about where you are stuck.
Is this where I get help? I am stuck on a problem on acceleration. First time on… 🙂
The problems are right after the lab on Driveway Races.
Problem 2: A car is decelerating at -5 m/s^2 from a starting speed of 15 m/s. How far does it travel? So a = -5; vi = 15… t calculates to 3 s. but I keep getting a negative number for distance. Same magnitude as the given answer, but different sign…. a negative distance??
If you haven’t yet completed Alg 1 & 2, then Ad Physics is going to be more challenging. I’ve put together an overview course to show you the basics, so please view it here: https://www.sciencelearningspace2.com/math/category/math-topics/algebra/ I’ve gone through the sample calcs in detail for Adv Physics so it will make sense, so please let me know if you still need help.
well, stuck already!
How do we calculate the formula?
Thank you!
Hello, I am also looking for the answers to the “acceleration problems”, with the work shown. We are having a little trouble understanding how to come to the correct answer, so if you have the work shown, I think it will help us. Thanks!
Hi there! Yes the up, the solutions are there, however I did not post the solutions to the specific labs, as the answers are going to change based on what you measure for the data table. I’ve sent you a private email.
Hello Aurora! I’m looking for the solutions to the lab problems. The answers are there, but the work that leads to the solutions is not. I saw Kimberly Voelkel asked the same question. Can you help me find that updated file you said you would post?
The answers are on the last page if it is a single worksheet download. If it is the BIG download from the high school section, they are listed as the last link in each lesson section.
Were do we find the answers to the homework questions? I see someone else had trouble finding them, but I do not know where they have been uploaded to.
Thanks
They are in parentheses on the back page.
Yes, it’s in one of the videos early in the course (look for p-t and v-t graphs). Take two points on the graph, and the slope is how much it changes vertically (rise) divided by the distance it changes horizontally (run).
Also my son was looking up how to calculate a slope for the graphs. Did you cover this somewhere that we missed?
Hello. Where can I find the answers to the acceleration problems worksheets?
Yes, did you do the experiment on Acceleration a few lessons back? I show you how to do a data table there. I notice that in a few lessons from now, there’s one on graphing, and I am wondering if I should move this one to after those graphing lessons. Here’s the section that includes graphing:
https://www.sciencelearningspace2.com/2014/10/vector-diagrams/
So I am wanting to do the experiment and I am looking at the pages that you have made for the data of the experiment. I can do the first part of the experiment but then it gets to the part were it wants me to graph it my data. I don’t know how to graph it. And I don’t know how to F = ma equation. Do you have anything explaining these things so I can do the experiment.
Thanks
One way to look at this is to notice the units in the equation.
Units for distance is in length, like feet.
Units for acceleration is length per time per time (or length per time squared). If we multiply acceleration by time twice, the time in numerator cancels with the denominator and we just get length back out.
The “1/2” is a little more complicated, and will make more sense when you get to calculus, but if you notice that the ball speeds up as it’s falling and the relationship between time and distance is a factor of 2.
Hello Aurora,
We did run the experiment and received a curve for the distance over time. I understand your equation of d=1/2a t^2 and how you changed it with the time squared and taking the half. This basically creates a new equation d = ax (which is a line). However I do not understand what I am doing physically by square the time and dividing it by half. Can you explain the background or is it explained later?
Thanks for the update!
We found the solutions to our question “A dog begins running and accelerates…”! Sorry about the confusion…..we got it now! 🙂
Oh gosh, you’re right – these are missing! I’ll get these fixed and post the updated file right away.
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. 🙂
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:
https://www.sciencelearningspace2.com/2014/09/introduction-to-kinematics/
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:
https://www.sciencelearningspace2.com/2014/09/scalars-and-vectors/
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!
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?
Thanks!