Velocity

A vector measurement of the rate and direction of motion. The scalar absolute value of velocity is speed.

In Classical mechanics (that is, when the velocities involved are significantly less than the speed of light) the average velocity of an object moving a distance d during a time interval t is described by the simple formula:

v = d/t.

Acceleration is the change of an object's velocity over time. It is defined as:

a = (v_f - v_i)/t

The final velocity of an object after accelerating at acceleration a for a period of time t is:

v_f = v_i + at

The average velocity of an accelerating object is (v_f + v_i)/2. To find the displacement of an accelerating objuect during a time interval, substitute this expression into the first formula to get:

d = t(v_f + v_i)/2

When only the object's initial velocity is known, the expression

d = v_it + (at²)/2

can be used. The basic equations for final velocity and displacement can be combined to form an equation that is independent of time:

v_f² = v_i² + 2ad

These simple equations become more complicated as velocities approach the speed of light, where the effects of general relativity starts to become significant.