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.

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* = 10 second mark, the line moves below the *x* axis to the point *y* = -10 m/s.

During straight line motion, a negative velocity means the object is moving backwards. So, what happened here is that the car is now driving backwards on the track. On a velocity vs. time graph, any time the line crosses the *x* axis, the object is changing direction.

To recap, the car was not moving, then accelerated to 20 m/s before maintaining this speed for 4 seconds. At this point, the car applied its brakes for 4 seconds, negatively accelerating until it stopped.

Once stopped, the car reversed direction and accelerated to 10 m/s in the opposite direction.You could easily describe all that in words but I think it’s much easier to simply draw a graph.

## Lesson Summary

Let’s briefly review velocity vs. time graphs.

You can determine a lot of information about the straight-line motion of an object by looking at the shape of the line on a velocity vs. time graph. A rising line represents an increase in velocity called acceleration. If the line is flat and horizontal, the object is traveling at a constant speed. A line that is falling towards the *x* axis represents an object that is negatively accelerating, or slowing down. When the line hits the *x* axis, the object has stopped moving.

If the graph continues below the *x* axis, the object has changed direction and is moving backwards at increasing velocity.

## Learning Outcomes

Following this lesson, you should be able to:

- Define velocity
- Describe how a velocity vs. time graph is set up
- Explain how to determine the straight-line motion of an object using a velocity vs. time graph