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# 4.5: Position-Time Graphs

Difficulty Level: At Grade Created by: CK-12
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Practice Position-Time Graphs

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Drawing line graphs can help you understand motion. In this article, you’ll learn how to draw distance-time graphs and how you can use them to find the average speed of moving objects.

Q: What’s missing from the graph being drawn in the picture above?

A: The x- and y-axes are missing.

### Graphing Distance and Time

The motion of an object can be represented by a distance-time graph like Graph 1 in the Figure below. In this type of graph, the y-axis represents distance and the x-axis represents time. A distance-time graph shows how far an object has traveled at any given time since it started moving. However, it doesn’t show the direction(s) the object has traveled.

Q: In graph 1 above, what distance has the object traveled by the time 5 seconds have elapsed?

A: The object has traveled a distance of about 25 meters.

### Slope Equals Speed

In a distance-time graph, the speed of the object is represented by the slope, or steepness, of the graph line. If the graph line is horizontal, like line B in Graph 2 in the Figure below, then the slope is zero and so is the speed. In other words, the object is not moving. The steeper the line is, the greater the slope of the line is and the faster the object is moving.

Q: In graph 2, which line represents a faster speed: line A or line C?

A: Line A represents a faster speed because it has a steeper slope.

At the following URL, explore distance-time graphs by doing one of more of the activities and simulations.

### Calculating Average Speed from a Distance-Time Graph

It’s easy to calculate the average speed of a moving object from a distance-time graph. Average speed equals a change in distance (represented by Δd) divided by the corresponding change in time (represented by Δt):

speed=ΔdΔt\begin{align*} speed= \frac{\Delta d}{\Delta t}\\\end{align*}

For example, in Graph 3 in the Figure below, the average speed between 1 second and 4 seconds is:

speed=ΔdΔt=3m2m4s1s=1m3s=0.3m/s\begin{align*} speed= \frac{\Delta d}{\Delta t}\\=\frac{3m-2m}{4s-1s}\\=\frac{1m}{3s}\\=0.3m/s\end{align*}

Q: In graph 3, what is the average speed between 0 and 4 seconds?

A: The average speed is:

speed=ΔdΔt=3m0m4s0s=3m4s=0.8m/s\begin{align*} speed= \frac{\Delta d}{\Delta t}\\=\frac{3m-0m}{4s-0s}\\=\frac{3m}{4s}\\=0.8m/s\end{align*}

### Summary

• Motion can be represented by a distance-time graph, which plots distance on the y-axis and time on the x-axis.
• The slope of a distance-time graph represents speed. The steeper the slope is, the faster the speed.
• Average speed can be calculated from a distance-time graph as the change in distance divided by the corresponding change in time.

### Vocabulary

• average speed

### Practice

Do problems 4a and 4b on the average speed worksheet at the following URL. http://www.mrjgrom.com/Physics%20resources/Speed_Problem_hw1.pdf

### Review

1. Describe how to make a distance-time graph.
2. What is the slope of a line graph? What does the slope of a distance-time graph represent?
3. Can a line on a distance-time graph have a negative slope, that is, can it slope downward from left to right? Why or why not?
4. In graph 1 above, the speed of the object is constant. What is the object’s speed in m/s?
5. In graph 3 above, describe the motion of the object at the time of 2 seconds.

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