### Accelerated Motion

As the position of a moving object changes with respect to time so does its speed.

The average velocity can be calculated if we consider the initial and final position of the object.

The object starts from rest, at time t_{1} where the object occupies position d_{1} and stops moving at time t_{2}, where it occupies position t_{2.}

Then the average speed of the object is calculated by:

Similarly, the average acceleration is given by the expressions below:

In many practical situations we can reduce some of the mathematical variables by taking into account two things:

a) the acceleration can be assumed to be constant (unless otherwise stated)

b) the initial time at which the observation of the motion started is zero -- t_{1}= 0

Therefore we can write:

or we can take t2 to be the total time t and simplify further

expressing the above equation as a product (instead of a division) is easier to analyze

............. **Equation of accelerated motion #1**