Main Page | See live article | Alphabetical index

Velocity is a vector measurement of the rate and direction of motion. The scalar absolute value (magnitude) of velocity is speed. Velocity can also be defined as rate of change of displacement.

In mechanics the average speed v of an object moving a distance d during a time interval t is described by the simple formula:

v = d/t.

The instantaneous velocity vector v of an object whose position at time t is given by x(t) can be computed as the derivative

v = dx/dt.

Acceleration is the change of an object's velocity over time. The average acceleration of a of an object whose speed changes from vi to vf during a time interval t is given by:

a = (vf - vi)/t.

The instantaneous acceleration vector a of an object whose position at time t is given by x(t) is

a = d2x/(dt)2

The final velocity vf of an object which starts with velocity vi and then accelerates at constant acceleration a for a period of time t is:

vf = vi + at

The average velocity of an object undergoing constant acceleration is (vf + vi)/2. To find the displacement d of such an accelerating object during a time interval t, substitute this expression into the first formula to get:

d = t(vf + vi)/2

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

d = vit + (at2)/2

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