# Graphs of Motion

by Jared Rovny

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00:01 The last thing I wanna talk about for this lecture is Graphs of Motion and how we visualize motion.

00:07 All this things I've talked about haven't really made a great picture yet.

00:10 But having these pictures in your head for how things move is very, very useful way of thinking about motion and then velocity and acceleration as well.

00:19 So here let us introduce a basic graph of how we plot things and learn how they move.

00:24 On this graph that you see on the left here, we have time on the x axis, where we're measuring time and seconds as we have time in zero seconds, 1 seconds, etc.

00:32 And on the vertical axis, we're plotting the position x in meters, so we have zero meters, 1 meter, 2 meter, etc. going up.

00:40 It's really important to understand that in this plot we're not saying that something is actually moving vertically by plotting its position.

00:46 All I'm doing is using the vertical axis to represent where the object is.

00:50 The physical actual situation you can see to your right in this problem, we're actually showing our object as time moves forward.

00:57 So looking at these intervals of time, let's see what this would look like.

01:00 Let's first take an object that's not moving.

01:02 If this apple is just sitting here at the position of 1 meter, then my graph looks like 1 meter at all times.

01:09 So as my time goes on my object is just sitting still and so as position stays at 1 meter as my time moves forward. So this is a nice boring graph that shows you exactly how you'll plot the position of an object that's not moving.

01:22 Now if we introduce some motion. Let's say that its moving 1 meter every second as you can see here, every seconds is moved from 1 to 2, etc.

01:29 Then I can plot the position of each moment by a different place on the graph.

01:35 So after 1 second, you can see from our physical picture that it's move from 1 to 2.

01:39 So after 1 second it's at a position of 2 meters.

01:43 Looking at the graph, what I've done is exactly that, at 1 second, I've plotted the point that is at 2 meters, because at the 1 second mark, our object is at the 2 meter mark in the physical situation so I put a point there.

01:55 And then I can do these for each subsequent second.

01:58 In the next second it goes to the second meter and then on the third second it goes to the fourth meter, etc.

02:03 So as we go second by second, meter by meter, I just put a point on our graph representing where our object is at each point in time.

02:09 And then we can connect all of our points that we plotted by a simple line.

02:14 In this graph you can see that the constant motion of an object represents, is represented by just a straight line whose slope gives us how fast the object is moving.

02:23 Then will show in a second how we can plot velocities and accelerations and what those mean in this context.

02:28 We need to do one more thing, which is what happens if I left the object accelerate, not moving in constant velocity but allow the velocity to change over time.

02:35 And we have the same kind of graph as we saw earlier.

02:38 We have an object that initially in the first second moves 0.5 meters and the next second it moves a meter, and on the 3rd second it moves 1.5 meters bringing it all the way to the 4 meter mark.

02:50 Plotting each of these points we can say that after 1 second it is at 1.5 meters, after 2 seconds it is at 2.5 meters, looking at the x axis on our green graph here, and then after the 3rd second it's gone all the way to the 4th meter.

03:06 So it's picking up speed and accelerating.

03:08 And you can see when we've given object acceleration rather than just motion, it picks, it gains are curve line rather than a straight line.

03:16 This is to indicate that the velocity of this object is picking up and getting faster and faster as we go.

03:22 But this is just meant to be an introduction to graphs and graphical representation of how objects move. So let's see how position, velocity and acceleration are related to each other.

The lecture Graphs of Motion by Jared Rovny is from the course Translational Motion.

### Included Quiz Questions

1. Each point on the graph represents a particular location at a particular time.
2. The vertical axis represents the vertical position of the object.
3. The horizontal and vertical axes must have the same units.
4. The horizontal and vertical axes represent position and velocity, respectively.
5. The graph is a visual “bird's-eye view” of the object.
1. The graph will not be a straight line.
2. The graph must be positive everywhere.
3. The graph can only be negative.
4. The graph will always be a straight line.
5. The graph must have an upward slope.
1. A straight line
2. A horizontal line
3. A curved line
4. A circle
5. A parabola

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