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

displacement equals velocity original times times plus one half times acceleration times time squared

Introduction

Where does this equation come from?

Algebraic rearrangements

Problems: [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]

Additional information

 

Velocity and Acceleration

velocity final equals velocity original plus acceleration times time

Introduction

Where does this equation come from?

Algebraic rearrangements

Problems: [ 1 ] [2 ] [ 3 ] [4 ]

Additional information

 

Time Independent Acceleration

velocity final squared minus velocity original squared equals two times acceleration times displacement

Introduction

Where does this equation come from?

Algebraic rearrangements

Problems: [ 1 ] [ 2 ] [ 3 ] [ 4 ]

Additional information

 

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