# Velocity

**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*.

**v**of an object whose position at time

*t*is given by

**x**(

*t*) can be computed as the derivative

**v**= d**x**/d*t*.

*a*of an object whose speed changes from

*v*

_{i}to

*v*

_{f}during a time interval

*t*is given by:

*a*= (*v*_{f}-*v*_{i})/*t*.

**a**of an object whose position at time

*t*is given by

**x**(

*t*) is

**a**= d^{2}**x**/(d*t*)^{2}

*v*

_{f}of an object which starts with velocity

*v*

_{i}and then accelerates at constant acceleration

*a*for a period of time

*t*is:

*v*_{f}=*v*_{i}+*a**t*

*v*

_{f}+

*v*

_{i})/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*(*v*_{f}+*v*_{i})/2

*d*=*v*_{i}*t*+ (*a**t*^{2})/2

*v*_{f}^{2}=*v*_{i}^{2}+ 2*a**d*

The kinetic energy (movement energy) of a moving object is linear with both its mass and the square of its velocity: