Kinematics Equations

Background Information

Vectors have magnitude AND position.

Variables that just have a magnitude are called scalar quantities.

Vectors can be denoted by a little arrow over their variable names, or by being written in boldface.


The Kinematics Variables

If we look at position as a function of time, the change in the position has a direction and magnitude, and thus can be considered a vector. This is called displacement.

x(t) = position as a function of time

∆ x = xf - xi = displacement. Units are the units of distance (m)


The change in the displacement with respect to time is a vector called velocity. The magnitude of the velocity is called speed.

Velocity is the displacement over time Units of velocity are units of speed (distance/time → m/s)

The change in the velocity with respect to time is a vector called acceleration.

acceleration is the change in velocityUnits of acceleration are (speed/time → m/s2)


The kinematics equations

“Name” of equation      
VAX vf2 = vo2 +  2a ∆ x
VAT vf = vo +  at
XAT ∆ x = vot +  ½ at2





*Things to note about the above equations:

  • The names help you memorize them. The first letter is the term on the left. The last two letters describe the second term. The first term is always a “vo” term. The units of the right-sided terms are always the same as the left-sided ones.
  • VAX is the only equation which doesn’t use time. Use it when you don’t know time.


Check out this page which goes through the derivation of these equations (note than on that webpage, they use the variable name “s” for displacement instead of ∆ x).


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