The Uniform Acceleration Motion

his is a motion during which the instantaneous acceleration is always constant.

(1)

A constant acceleration reveals that:
1)the direction of motion is along a straight line.
2)Average acceleration and instantaneous acceleration have the same magnitude:

By coupling the last relationship with the definition of average acceleration, we can build the velocity law for a uniform acceleration motion



If  then , and the last one can be written as

(2)

The velocity versus time graph is a straight line and its angular coefficient is the motion’s acceleration .

From this graph the relationship between the average velocity and the instantaneous velocity can be deduced. It follows from the idea of a segment’s average point:

By coupling this with the previous equation (2) and with the definition of average speed, we have a three equation system. Its solution represents the law of motion for uniform acceleration motion:

By inserting the (b) into the (a) we have:

and by inserting the (c) into the last one:

that leads to:

(3)

The graph of this motion law is a branch of a parabola. For instance, if the initial distance  and the initial velocity  are equal to zero, the diagram is similar to the following one:

The parabolic behaviour is strictly related to the square dependence on time