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# Graphs of Motion

###### Matt Jones

###### Matt Jones

**M.Ed., George Washington University**

Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

The two most commonly used **graphs of motion** are velocity (distance v. time) and acceleration (velocity v. time). In each case, time is shown on the x-axis. The graph of velocity is a curve while the graph of acceleration is linear. The slope of a line tangent to the graph of distance v. time is its instantaneous velocity. The slope of a line tangent to velocity v. time is its acceleration.

Let's talk about graphs of motion. There's two types of graphs that you're going to have to make for Physics involving motion.

The first one is distance over time and we know distance over time really equals speed or velocity. The other one is velocity over time and of course you know that velocity over time is is another way of saying acceleration okay. Well let's look at how these graphs are going to look okay.

First let's look at a graph of a constant velocity okay in this case we're going 5 meters per second okay? So if we go 5 meters per second for 4 seconds the first second we're at 5 meters the second 10 third second 15 and the fourth 20 seconds so I just draw a nice straight line okay and again I've got a constant velocity right? My velocity is increasing at 5 units per second okay? So in this case we look at the graph and we analyze the slope the rise over run, what the rise over the one is telling us is that slope of 5 here equals 5 meters per second okay? One point about graphs when we do motion graphs we always want to put time on the x axis and distance or velocity or speed on the x axi- I'm sorry on the y axis so time is always on the x okay? So just make sure you always do that when you're doing your graphs okay.

Well, looks at a graph of acceleration, and here we have the acceleration of a free falling object okay? So it's the acceleration of force of gravity pulling it down okay so on on this graph I'm going to start with [IB] unit 0, the first second it's going about the same to 5 but I know acceleration starts slowing and steadily increases okay? After 2 seconds I'm up here at close to 20 at 3 close to 30 and at 4 I'm right up here close to 80 okay? So notice here my velocity is not remaining the same, my velocity is increasing and it's increasing at an increasing rate okay? How can I calculate the velocity at any given point on that acceleration curve? Well for any point I can draw a tangent line and that'll tell me what the velocity as at that specific moment so calculating from a tangent line the rise over run will tell me the specific velocity at that point okay? Alright so thatÃ¢Â€Â˜s how we calculate distance over time graphs.

Now let's look at a graph that would involve velocity over time so I need to change the units on my y axis so we're not looking at distance over time, this time we're looking at velocity or speed and remember speed and velocity are let's say velocity is what? Meters per second okay so now with my two sets of data, they don't look like different okay so on this one I've got a constant velocity of 5 meters per second, so when I come over here the 5 and I'm going to stay 5 meters per second, the velocity does not change so in this case the velocity or slope I'm sorry, the acceleration is 0 I have a constant velocity which equals 0 acceleration okay? Now let's look at the falling object okay? Here I've got the object with increasing rate and but the acceleration is constant, the acceleration again is 9.8 meters per second squared which is almost 10 so if I draw that line, after 1 second I'm at almost 10 at 2 seconds I'm at almost 20 at 3 seconds I'm at almost 30, I try get my graph correct, and at 4 I'm at almost 40, 4 and 40 right there so if I draw this now notice I have a straight line that's increasing and it's increasing at about 9.8 meters per second that's the increase every second in velocity so when I graph velocity versus time if I have something that's accelerating what it shows me is it shows the constant increase okay if I have something at a constant speed or velocity it shows me something that's not changing that speed is remaining the same, the slope is 0. So these are two graphs that you're going to have to use in calculate, in Physics.

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###### Matt Jones

M.Ed., George Washington University

Matt is very comfortable in front of the whiteboard and is able to make every topic easy for anyone to digest. His straightforward approach to teaching is very refreshing.

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## Comments (2)

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## Melisa · 11 months, 2 weeks ago

This is so beneficial, but can you add an acceleration-time graph?

## Susan Moore · 11 months, 3 weeks ago

Perhaps demonstrate a negative acceleration?