Practice Calculating Velocity & Acceleration

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  • 0:03 Two Types of Velocities
  • 3:17 Acceleration
  • 3:56 Displacement vs Time Graphs
  • 4:49 Acceleration vs Time Graph
  • 5:30 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

Kinematics is the study of motion. In this lesson, we will practice calculating the two types of velocity and acceleration. Also, we will be looking at graphs of displacement vs. time and acceleration vs. time.

Two Types of Velocities

When you are driving in your car, the speedometer tells you your instantaneous speed, which is the speed you are traveling at that instant in time. Most modern cars have the feature where your average speed is given, which is the total distance you have driven divided by the time it took to drive that distance. I am using the word 'speed' because the speedometer and the car's computer do not report the direction you are going along with the speeds. Velocity is a vector and requires speed and direction.

Average Velocity

The first type of velocity we will look at is average velocity, or an object's displacement over a period of time. Determining average velocity only requires the use of the equation:


Example 1

Here's an example:

Determine the average velocity of an object that traveled 30 meters north, 20 meters south, and then 15 meters east in 20 seconds.

First, we need to determine the displacement of the object, which requires the vector addition of the distances. Let's assign j to be a vector pointing north and i to be a vector pointing east.


Numerically determining the displacement, we get:


Note that we replaced 20 meters south with -20 meters north. This means our total displacement s is equal to 15 meters east plus 10 meters north.

Now we can plug the displacement and travel time into the average velocity equation:


Instantaneous Velocity

Determining instantaneous velocity, or an object's velocity at a specific point in time, is a little more involved. If the position of an object varies with time, we can take the first derivative of the position-time function to determine the instantaneous velocity at any time.

There are a few steps to take a derivative:

1. Multiply the coefficient of the variable by the exponent on the variable, and write that number as the variable's new coefficient.

2. Lower the original exponent by 1, and write that as the new exponent.


  • C is the coefficient.
  • t is the time variable.
  • n is the exponent on the time variable.

3. Do steps 1 and 2 for each part of the equation that has the variable t in it. The derivative of constants is zero.

Example 2

Let's do an example:

A mass in an experiment has the position function:


Determine its velocity at 6 seconds.

Taking the derivative of this function will give us the velocity function at any time. Following the derivative rules, we get


To solve the problem, all we have to do is plug in 6 seconds in for time:



Acceleration is the change in velocity divided by the time required for the change. To determine instantaneous acceleration, you would take the derivative of the velocity-time function and plug in any time. Let's do an example.


Example 3

Let's do an example:

It takes an object 6 seconds to go from 396 m/s to 1656 m/s in the x-direction. What is the object's average acceleration?

Using the average acceleration equation, we get:


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