The velocity kinematics equation is used for objects that are moving in one dimension with a constant acceleration.  An example would be a vehicle that is travelling on a straight road with a given acceleration.  We can use the equation to determine the velocity after it has accelerated for a given amount of time.

The velocity kinematics equation. vee sub x equals vee sub x naught plus A sub x times tee.
The Kinematics Velocity Equation.

Variables in the Kinematics Velocity Equation

This equation relates the initial speed, the final speed, the acceleration, and the amount of time that an object moves with a constant acceleration.

  • vx represents the final speed of the object.
  • vx0 represents the initial speed of the object
  • ax represents the acceleration of the object
  • t represents the time interval of the accelerated motion.

Units in the Kinematics Velocity Equation

The velocity kinematics equation. vee sub x equals vee sub x naught plus A sub x times tee.
The units for each of the three terms are meters per second, meters per second, and meters per second squared times seconds.
  • vx has units of meters per second (m/s).
  • vx0 also has units of meters per second (m/s).
  • ax has units of meters per second squared (m/s²)
  • t has units of seconds (s).

Notice that each of the terms ultimately ends up as meters per second. The term with acceleration times time has units of m/s² times s, which simplifies to m/s.

If you are using other groups of variables, make sure that they are consistent.  In particular, make sure that the time units in the acceleration and time match.  For example, if you have a time given in minutes, make sure that you change that time to seconds.

Also make sure that the distance units match.  You could use MPH for the speed units and MPH/s for the acceleration.  Both of these units have miles as the distance part of the units.

Make sure that all units are in either metric or imperial units.  For example, don’t mix MPH and km/s without converting into a common set.

Things to Watch Out for in this Equation

This equation only works when the acceleration is a constant.  If the acceleration changes during the motion, you’ll need to break the motion into parts.  Each part would be a section where the current acceleration is constant.

Note that the time in this equation actually represents a period of time.  If you are given a starting time and an ending time, you need to subtract the two times to produce a time interval.  Many textbooks represent “t” in this equation as “Δt”.