Kinematics, Equations for Accelerated Motion

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In introductory mechanics there are three equations that are used to solve kinematics problems:

Displacement equation

Final velocity equation

Time independent equation


These three equations are explained below. For each equation we will:

  • Present an introduction.
  • Understand a derivation, or origin.
  • Use algebra to rearrange and solve the equation for all of its variables.
  • Do some random valued multiple-choice problems.
  • Cover some details and additional information.


Symbols used in these equations:

d Displacement or change in position
vo Original velocity, the velocity at the start of the acceleration
vf Final velocity, the velocity at the end of the acceleration.
a Acceleration, this is a constant acceleration
t Time


There are many cross links in the discussions that follow.

If you get lost, at the top of each discussion page is a link back to this page, the home page for these equations.

So if you need to, you can always jump back to here for a clear starting point in your navigation.


Displacement and Acceleration


Velocity and Acceleration


Time Independent Acceleration


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