Acceleration#Uniform acceleration

A uniformly accelerated motion is a motion in which the acceleration is constant with respect to strength and direction. The uniformly accelerated motion is a linear motion when acceleration and top speed are collinear. This is not the case, is formed as a parabolic trajectory. By the choice of an inertial system, in which the initial velocity is zero, is obtained always in a straight line. When the acceleration becomes zero, we obtain the uniform movement.

Examples of a uniformly accelerated motion are the free fall or the oblique throw without consideration of air resistance.

Legislation

If the uniformly accelerated motion is linear, one can for calculations numbers ( scalars ) instead of vectors used ( Skalarform ). It is sufficient to express the orientation of the velocity and the acceleration vector by the sign. A direction (usually the direction of movement) is recognized as a positive, the opposite direction as negative.

Passing the uniformly accelerated motion is not a straight line, the more general form of vector to be used. Apply the following laws:

Derivation

From

Obtained at constant acceleration by integrating a linearly dependent on the time rate:

Wherein the integration constant, which includes the initial velocity.

It is further known that the speed is the first derivative of the position with respect to time:

Subsequent integration yields the position:

Wherein the initial position.

The equations for the velocity and the position thus read: