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Straight Line Displacement-Time Graph

We will begin with the simplest type of motion graph, the displacement-time graph. A displacement-time graph, like the one shown here, puts timemeasured in seconds along the x-axis. On the y-axis is the displacementusually measured on meters .

Displacement at 2 seconds

Let's take a look at this graph carefully to see what we can learn about the object's motion.

After 2 seconds, what is the displacement of the object?

Answer: After 2 seconds, the displacement is 2 meters, as shown on the graph by the yellow dot.

Displacement at 5 seconds

Try another question about this graph.

After 5 seconds, what is the displacement of the object?

Answer: After 5 seconds, the displacement is 5 meters, as shown on the graph by the yellow dot.

Is the object moving?

Hopefully, you see the correlation between the displacement and the line on the graph. From 0-5 seconds, this object is continually increasing its displacement. So what can we say about that object?

Well, obviously, it must be MOVING!

If its displacement is increasingbecoming more positive the object must me moving. It is moving towards the positive direction usually right or upwards .

Object's Velocity from 1 to 5 seconds

This means that they slope of this line also shows us the object's velocity. If at 1 s the object has traveled 1 m, and at 5 s the object has traveled 5 m, then the object is moving at a rate of 1 m/s. And, since the displacement is getting greater or increasing, we know that motion is in the positive direction.

You may also recognize that as the slopechange in y-axis divided by the change in x-axis of the line.

Displacement from 5 to 10 seconds

Now let's move to the next portion of the line.

From 5 s to 10 s, what happens to the object's displacement?

Answer: It stays the same; it does not change, as shown by the highlight.

Is the object moving or stopped?

You should see from the straight line that the displacement of the object does not change from 5 s to 10 s.

What does this mean?

It means the object has STOPPED or is no longer moving. Since no displacement is happening, the object must be stationarynot moving .

Velocity from 5 to 10 seconds

What does this now say about the velocity of the object? Since the object has stopped, the velocity must be 0 at this time (from 5 s to 10 s).

Remember, velocity is represented by the slope. Since there is no slope from 5 s to 10 s, that also indicates that velocity = 0.

Displacement from 10 to 12 seconds

Now let's move to the final portion of the line (10 s to 12.5 s). This can get tricky, so pay close attention.

What happens to the displacement of the object from 10 s to 12.5 s?

Answer: It decreases from 5 m to 0 m, as shown by the highlight.

Is the object going forwards or backwards?

The displacement along this last portion of the graph is decreasing. Remember, if displacement is negative (-) or decreasing, that means the object has turned around and is going backwards or back to where it began.

Total Displacement

Since this object's graph ends back at the x-axis, it means that this object returned to its original position. The total displacement of this object from 1 s to 12.5 s is actually 0 meters.

At 0 seconds (circled in green), the object's displacement is 0 m. At 12.5 seconds (circled in orange), the object's displacement is 0 m again. Final position (0 m) - initial position (0 m) = Change in displacement (0 m).

Velocity from 10 to 12.5 seconds

Notice that the slope of this line is negative which also indicates that they displacement is in the opposite direction. What does this say about the velocity from 10 s to 12.5 s?

Since velocity = slope, the object does have a velocity at this point, but that velocity is negative (or in the opposite direction).

Also notice that the slope of this portion of the line is greater than (steeper) than the section from 0 s to 5 s. This means that the object is moving with a greater velocity during this time than during the first 5 s of travel.

Review

Let's review what we have learned so far about straight line displacement-time graphs:

Take a look at The Passing Lane animation from The Physics Classroom to see two cars moving and the displacement-time graph of the movement. Make sure to read about the graph as well.