Technically, this model is applicable to a single point particle subject to a constant acceleration that is either parallel to or anti-parallel to the particle's initial velocity. Its real usefulness lies in the fact that it can describe mutli-dimensional motion with constant acceleration if the motion along different orthogonal directions is treated by application of the one-dimensional rules independently along the differect axes. Thus, it can be used describe the system's motion in any situation where the net force on the system is constant (a point particle subject only to near-earth [gravitation] is a common example). It is a subclass of the One-Dimensional Motion (General) model defined by the constraint da/dt = 0.

For pure kinematics situations, the problem will often explicitly state that the acceleration is constant, or else will indicate this bu giving some quantitative information that implies the acceleration is constant (e.g. a linear plot of velocity versus time). This model is always applicable to the vertical direction in a problem that specified gravitational freefall. The model is also sometimes useful (in conjunction with Point Particle Dynamics) in dynamics problems when it is clear that the net force is constant.

• 1-D Motion (Constant Velocity)

• [position (one-dimensional)]
• velocity
• acceleration

A single point particle (or a system treated as a point particle with position specified by the center of mass).

Some constant external influence must be present which produces a constant acceleration that is directed parallel or anti-parallel to the particle's initial velocity.

This model has several mathematical realizations that involve different combinations of the variables.

• Position as a Function of Time
  From the formulas given in the Laws of Change, it is clear that a plot of position vs. time will give a parabola.

If the acceleration is positive the parabola will open upwards. The position at t = t_i will be x_i , as shown in the graph below (time at the origin is t_i ):

In this case the position is positive. The fact that the plot of position vs. time is increased means that the initial velocity, v_i , is also positive.

If the acceleration and the initial position x_i were the same, but the initial velocity was negative , then the graph of position vs. time would look like this:

The parabola has a minimum value at the time t_min

This information is intended to familiarize the reader with the shape of the curve and how it behaves. Obviously, if the object starts out at time t = t_i its real motion will not be described by the portion of the curve for t < t_i, and so an object moving with positive initial velocity and positive acceleration will not have such a "minimum" position – it will move in the same direction, with uincreasing speed, for all *t > t_i.

On the other hand, an object with negative initial velocity v_i and positive acceleration will encounter a "minimum" position at which it will have zero velocity, after which it will reverse direction and gather speed with increasing time.
For the case of positive acceleration, with positive non-zero velocity at t = t₁ and non-zero position x₁ this will appear as:

• Velocity versus time graph

A plot of velocity vs. time, with positive velocity at t₁, is given by: