This position kinematics equation overview will help make sure that you are familiar with this important equation.

Kinematics Position Equation

Overview of the Equation

This 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 how far the vehicle has traveled after it has accelerated for a given amount of time.

Variables in the Kinematics Position Equation

The kinematics position equation is given by the final position equals the initial position plus the initial velocity times the time interval plus one half times the acceleration times the time interval squared.

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

  • x represents the final position of the object.
  • x0 represents the initial position 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 Equation

The units in each term of the kinematics position equation are meters, meters, meters per second times meters,  and meters per second squared time seconds squared.

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

  • x has units of m.
  • x0 also has units of m.
  • vx0 has units of m/s.
  • ax has units of m/s².t has units of seconds.

Notice that ultimately, each added term in this equation has units of meters. For example the term vx0 t has units of m/s times s which becomes m.

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.  

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.