### Video: Velocity vs. Time Graphs

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V-t Graphs: Constant Speed Motion || V-t Graphs: Changing Speed Motion

#### Velocity vs. Time Graphs

Video Transcript

Introduction
It's common to use a graph to represent an object's motion. A velocity vs. time graph (or v-t graph) is a common Physics graph. How do you interpret a v-t graph? How can you tell positive from negative velocity? How can a constant velocity be distinguished from a changing velocity or an at rest object? And how does slowing down look different than speeding up? I'm Mr. H and I have some answers for you.

Position-Time Graph Confusion
It's not unusual to confuse v-t graphs with position-time graphs (or p-t graphs). A student might see this v-t graph and think "the object is at rest" or this v-t graph and think "the object is moving with a constant speed" or this v-t graph and think "the object is slowing down". These are all incorrect statement that result from confusing p-t and v-t graphs. If these lines were all moved onto a p-t graph, each one of the interpretations would be correct. To avoid this mistake with motion graphs, always check the vertical axis first. Then use the right set of rules for that type of graph.

Interpreting Graph Features
Positive Velocity vs. Negative Velocity
So let's discuss the rules for interpreting a v-t graph beginning with the rule for distinguishing moving in the + direction from moving in the - direction? An object that moves in the + direction has a + velocity. So if you use your Math Noodle, you would reason that such an object is represented by a line in the + region of the v-t graph. Like this horizontal line ... or these diagonal lines ...or these curved lines. All these objects have a + velocity. And similar reasoning leads to the conclusion that an object moving in the - direction is represented by a line in the - region of the v-t graph like any of these lines ... shown here.

Constant Velocity vs Changing Velocity; Fast vs. Slow vs. At Rest
Some objects move with a constant velocity; others are accelerating ... or changing velocity. When you use your Math Noodle, you would reason that a constant velocity motion would be represented by a line that always keeps the same velocity value ... like this line or that line or even this line. Horizontal lines describe constant velocity motions. Now consider that there are numbers along the axis. Our three lines describe three different constant velocity motions. Object A moves in the + direction with a speed of 10 m/s.  It's faster than Object B which moves in the + direction with a speed of 5 m/s. And Object C has a velocity of 0 m/s; it is at rest ... not even moving

You must be careful when the horizontal line is in the - region. Objects D and E are both moving in the - direction at constant velocity. But Object E has the larger speed at 10 m/s. It is moving faster than Object D. So in conclusion, constant velocity objects are represented by horizontal lines. And the fastest of these constant velocity objects are furthest from the v = 0 m/s mark. The slowest objects are closest to v = 0 m/s.

Speeding Up vs. Slowing Down
Now let's contrast speeding up with slowing down. We'll begin with objects moving in the + direction ... having lines in the + region of the graph. Object A is a speeding up object; it's getting faster. It starts at rest (0 m/s) and finishes moving at a speed of 10 m/s in the + direction. And Object B is slowing down or getting slower. It starts with a speed of 10 m/s in the + direction and slows down to 0 m/s; it's stops. Object C is also speeding up and Object D is also slowing down. They're just changing their speed at a varying rate.

Once more, caution is required for lines in the - region. You must recognize that the - sign indicates a direction. A velocity of -10 m/s doesn't mean 10 m/s less than 0. The negative means moving in the negative direction ... such as leftward or westward or downward or ... whatever direction is considered the negative direction. So the -10 m/s is accurately interpreted as moving 10 m/s in the negative direction (e.g., in the leftward direction). Given this reasoning. Object E is getting faster. It starts at rest and finishes with a speed of 10 m/s in the - direction; We can say that Object E is speeding up. Object F must be getting slower or slowing down. It starts moving in the - direction with a speed of 10 m/s and finishes at rest. Objects G and H are also speeding up and slowing down, just doing so at a varying rate.

Changing Directions
One final motion to discuss is a turning around or a changing direction motion. Once more you need to use your Math Noodle. An object that changes direction is moving in one direction initially and then at a later time has turned around and is moving in the opposite direction. Put another way, it first moves with + velocity and later moves with a - velocity like this ... or vice versa like this ... . The point in time at which the line crosses from the + region to the - region of the graph (or vice versa) is the point at which the object changes direction.

Conclusion
Interpreting velocity-time graphs can be tricky. But knowing your rules and using your Math Noodle will turn you into a Physics Wizard. To make sure that you got this, I'd like to invite you try one of the interactive exercises on our website. You'll find links to them in the Description section of this video. They're pretty awesome! Hey I'm Mr. H, thanks for watching.

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