# Using Velocity vs. Time Graphs to Describe Motion

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• 0:03 Our Next Step In Kinematics
• 0:32 Velocity vs. Time Graph
• 1:26 The Shape of a…
• 4:03 Lesson Summary

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Lesson Transcript
Instructor: Angela Hartsock

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

In this lesson, we will look at an example of a velocity vs. time graph. By examining the shape of the graph, it is possible to accurately describe the motion of an object, even if that motion is very complex.

## Our Next Step in Kinematics

First, we used displacement and time to determine velocity, algebraically. We moved on from there to using velocity and time to calculate acceleration, algebraically. Then, we shifted gears and used data points of displacement and time to calculate velocity, graphically. It should come as no surprise that our next step would be to use data points of velocity and time to describe acceleration. So, let's dive in.

## Velocity vs. Time Graph

At first glance, a graph of velocity vs. time might look a lot like the graphs of position vs. time we've been working with. In fact, they are set up nearly identically. We use the same x, y coordinate system, the same shape, and the same time variable on the x axis. The only difference is instead of position, with the unit meters, on the y axis, we use velocity with m/s units. That's the basic velocity vs. time graph.

Remember, what we are describing with these graphs is the motion of an object in a straight line. Velocity is a vector quantity, requiring a magnitude and a direction. But, with straight line motion, the only directions we have to worry about are forwards and backwards. When the object is moving forwards, we call it positive. When it's moving backwards, we call it negative and so those values need a negative sign.

## The Shape of a Velocity vs. Time Graph

You will definitely have to make a velocity vs. time graph for one of your exams, and you should expect to answer several basic questions about the shape of the graph. Fortunately, these graphs are very easy to read, once you understand what's going on. Let's take a look at an example graph representing the motion of a car on a straight track.

As you can see above, we have velocity on the y axis and time on the x axis. As the car starts moving, the velocity changes from 0 m/s to 20 m/s between t = 0 s and t = 2 s. Hopefully, you remember that a change in velocity is called acceleration. So, a rising line on a velocity vs. time graph represents that the object is accelerating. Since the velocity is increasing, the acceleration is positive.

Now, look at the graph below between t = 2 s and t = 6 s. What's going on here? The car is driving at a constant velocity of 20 m/s for 4 seconds. So, a flat, horizontal line means that the velocity is constant and the object is not accelerating.

At the t = 6 s mark, the graph turns and starts moving downward. The velocity values are decreasing from 20 m/s at 6 seconds to 10 m/s at 8 seconds as the car applies its brakes. At t = 10 seconds, the car stops when the velocity hits 0 m/s. A line moving down towards the x axis represents that the object is slowing down. We call this type of motion negative acceleration.

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