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/s
2) or "feet per second squared" (ft/s
2).
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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:
- 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)
For advanced students, you will also need: a timer or stopwatch, pencil, paper, measuring tape or yard stick, and
this printout.
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
- 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...
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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.
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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
