Define an expression for distance travelled by a body with uniform acceleration.

Acceleration is the measure of velocity change, mathematically it is expressed as   where is time, is the velocity and is the acceleration. Note that velocity is a vector quantity and therefore acceleration is a vector, too. Velocity, in turn, is the derivative of displacement (also a vector quantity).

If the acceleration of a body is a constant vector, its velocity and displacement are collinear with the acceleration, so the movement is along a straight line. This line is suitable for projection as an axis. Denote the magnitude of the acceleration as the speed at as and let the starting position to be zero.

Integrating the equality we obtain integrating we obtain This is the distance travelled since The distance travelled between moments and is