### Video: Match That Graph

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#### Match That Graph

Video Transcript

Introduction
If you're given a position-time graph for a motion, how do you identify what the velocity-time graph would look like? Or if you're given the v-t graph, how do you know what the p-t graph would look like? I'm Mr. H. and I have some answers for you.

The Strategy
Graphs are used to describe an object's motion. They tell us if the object is moving or not moving, if the motion is a constant speed, speeding up or slowing down motion, and whether the object is moving in the "positive" or "negative" direction. The trick to matching a p-t graph to a v-t graph or vice versa is to first translate the graph to words. Then you can translate the words to the features of the target graph.

Position-Time Graphs <==> Verbal Descriptions
So how do you translate graphical info to a verbal description? We have several videos that extensively describe the relation between graphs and motion. So in this video, I'm approaching the topic as though you are not at Ground zero but know a little something about the topic. I'm going to go faster. If that's not the case, one of the links on the screen might serve you better.

When you interpret a p-t graph you want to know the answer to 4 important questions ...
• Is the object at rest or moving?
• If moving, is the object moving with constant speed or changing speed?
• If changing its speed, is the object speeding up or slowing down?
• A + or - sign is often used to represent a direction of a vector like velocity. Is the velocity + or -?

So here's the skinny on p-t graphs. An at rest object is represented by a horizontal line on a p-t graph. Moving objects are represented by lines that have a slope that is either + or  -.

Constant speed objects are represented by straight lines like these graphs. Changing speed objects are represented by curved lines.

Objects that are changing their speed are either speeding up or slowing down. Begin at the first point on the graph and read towards the right; observe whether the line is becoming steeper or flatter. Lines that become steeper with increasing time represent speeding up objects. Lines that become flatter with increasing time represent slowing down objects.

Lines that have a + slope (slope upward) represent objects that are moving in some pre-defined positive direction (like right or up). Lines that have a - slope (slope downward) represent objects that are moving in a negative direction (like left or down).

As an example, suppose you have this p-t graph and you want to match it to a v-t graph. So look at the graph and describe the motion ... in words ... using the 4 important questions. The object is moving (non-horizontal line). The object is changing its speed (curved line). The object is getting faster or speeding up (line becomes steeper). The object is moving in the - direction (line slopes downward). Now I need to know how to relate this description of an object's motion to v-t graph features.

Velocity-Time Graphs <==> Verbal Descriptions
So here's the skinny on v-t graphs. At rest objects have a velocity of 0 m/s; the line is on the axis. Moving objects are represented by lines above or below the axis.

Constant speed objects are represented by horizontal lines. Changing speed objects are diagonal lines (usually) and sometimes curved lines.

A line that continues further from the v=0 mark as time progresses is speeding up or getting faster. A line that starts far from the v=0 mark and gets closer to it is slowing down or getting slower.

Any straight or curved line in the + region of the graph has a + velocity. Any line in the - region of the graph has a - velocity.

So back to our example problem. The object is moving so the line is above or below the axis. The object has changing speed so the line is diagonal (not horizontal). The object is getting faster, so the line starts near the axis and moves further from it. The velocity is negative so the line is in the negative region of the graph.

If you're given a v-t graph and must find the matching p-t graph, then use the same strategy. Change the v-t graph to words and the words to a p-t graph. Hey. You got this!

Conclusion
When you get the feel for this strategy, you're going to be a Physics Wizard when it comes to matching p-t and v-t graphs. To make sure you got this, try an interactive exercise on our website. You will find links to them in the Description section of this video. Hey I'm Mr. H. Thanks for watching!

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