Graphs are used all over the field of physics, and the p-t and v-t graphs are the ones used most for moving objects, especially when describing the projectile motion of objects. With one peek at the graph, you can tell a lot about what's going on, which is one reason they are so useful. You don't have to pour over pages of equations to get a sense of what's going on with the experiment.

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Click here to go to next lesson on The position-time "p-t" graph.

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The position-time “p-t” graph is one that gets used a lot, and since it's axes are position and time, the slope of the line will give average velocity to describe the motion of an object.  If the velocity is constant, then the slope is constant and you'll see a straight line (either uphill or downhill). If velocity is changing, you'll see a curved rather than straight line for the slope. A steeper line indicates larger velocity. An uphill slope means positive velocity, downhill indicates negative velocity. If the slope is downhill and curved, but it starts out like a skier on a bunny hill, then the negative velocity starts slow and moves fast as time goes on, which is a sign of negative acceleration (starting slow and speeding up). If the slope looks instead like starting at the top of a black diamond run, then the object starts with a high negative velocity but ends with a slower velocity, a indication of positive acceleration.

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Click here to go to next lesson on The velocity-time "v-t" graphs.

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The velocity-time “v-t” graphs are another common type of graph you'll run across that describe motion of an object. The shape and slope of the lines on the graph will tell you a lot about what's going on with the motion of the object, and here's how you decipher it:  If the line is a straight, horizontal line, then the velocity stayed constant and there's no acceleration, like when you're driving on the freeway. Your car is moving at a steady 65 mph in a straight line.

However, if you're at a stoplight that just turned green, you're going to start changing your velocity by increasing your speed, giving you a positive acceleration. The graph will be a straight line starting at the origin and moving uphill. The slope of the line is positive, indicating your positive acceleration.

So can you tell if an object is moving in a positive or negative direction? Yes! A positive velocity means an object is moving in a positive direction, so if the line is in the positive region of the graph, you know it's traveling in a positive direction.  By the same logic, if the slope is in the negative regions of the graph, the object is traveling in a negative direction. For slopes crossing the axis, the object is changing directions.

Can you figure out if an object is speeding up or slowing down? Yes again! Speeding up means that the magnitude of the velocity is increasing in value (the number only, ignoring the plus or minus sign), so if the line is moving away from the x-axis, it's speeding up. And if it's approaching the x-axis, it's slowing down.

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Click here to go to next lesson on Slope of the Line.

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soccerball1This 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: [am4show have='p8;p9;p12;p39;p92;' guest_error='Guest error message' user_error='User error message' ] 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

  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...

[/am4show][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.

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Click here to go to next lesson on Describing Motion with Equations


Mechanics is the study of the motion of objects. This is a great place to start your studies in physics since it’s such a BIG idea. We’ll be learning the language, laws, concepts, and principles that explain the motion of objects. We’re going to learn about kinematics, which is the words scientists use to explain the motion of objects. By learning about scalars, vectors, speed, velocity, acceleration, distance, and more, you’ll be able to not only accurately describe the motion of objects, but be able to predict their behavior. This is very important, whether you’re planning to land a spaceship on a moon, catapult a marshmallow in your mouth from across the room, or win a round of billiards.


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Click here to go to next lesson on Scalars and Vectors.


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