The Velocity Squared Kinematics Equation

Kinematics velocity squared equation:  vee sub ex squared equals vee sub ex naught squared plus two times A times the quantity ex minus ex naught.

The velocity squared 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 over a certain distance.  Notice that this equation doesn’t have time.  This is useful when time isn’t provided directly in the information describing a situation.  The other two kinematics equations can be combined to produce this one.

Variables in the Velocity Squared Kinematics Equation

Velocity squared kinematics Equation variables:  final speed squared equals the initial speed squared plus two times A times the change in position.

This equation relates the initial speed, the final speed, the acceleration, and initial and final positions of an object that 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.

x represents the final position of the object.

x0 represents the initial position of the object.

Units in this Equation

The velocity squared equation units.  (Meters per second) squared equals (meters per second) squared plus meters per second squared times meters.

You can use this equation with many different combinations of variables.  Usually we use the following combination.

vx has units of m/s.

vx0 also has units of m/s.

ax has units of m/s².

x has units of meters.

x0 also has units of meters.

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 the distance units match.  For example, if you have an acceleration given in m/s², make sure that the distances are in m.

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 without converting into a common set.

Notice that each term has units of meters squared per seconds squared.

Things to Watch Out for in the Velocity Squared Kinematics 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.  Make sure to keep track of the twos in this equation.  The velocities are squared and there is a 2 in the last term.

If you are solving for one of the velocities, don’t forget to take the square root at the end. For example, many students have given an answer of 25 m/s when they really should have reported 5 m/s.