In kinematics, four

**equations of motion**(or

*kinematic equations*) apply to bodies moving linearly (in that is, one dimension) with uniform acceleration.

The body is considered at two instants in time, one "initial" point and one "current". Often, problems in kinematics deal with more than two instants, and several applications of the equations are required.

The body's initial speed is denoted . Its current state is described by:

- , the distance travelled from initial state
- , its velocity at this time
- , the time between the initial and current states

*a*, or in the case of bodies moving under the influence of gravity,

*g*.

Table of contents |

2 Extension 3 Rotation |

## Examples

Many examples in kinematics involve projectiles, for example a ball thrown upwards into the air.
Given initial speed *u*, one can calculate how high the ball will travel before it begins to fall.

The acceleration is normal gravity *g*. At this point one must remember that while these quantities appear to be scalars, the direction of displacement, speed and acceleration is important. They could in fact be considered as one-dimensional vectors. Choosing *s* to measure up from the ground, the acceleration *a* must be in fact *-g*, since the force of gravity acts downwards and therefore also the acceleration on the ball due to it.

At the highest point, the ball will be at rest: therefore *v* = 0. Using the 4th equation, we have:

## Extension

More complex versions of these equations can include a quantity *s*_{0} for the initial position of the body, and *v*_{0} for *u* for consistency.

## Rotation

The analogues of the above equations can be written for rotation: