1. The four kinematic equations which describe an object's motion are:
There are a variety of symbols used in the above equations and each symbol has a specific meaning.
d – the displacement of the object. (we use “x” & will also use “y”)
t – the time for which the object moved.
a – the acceleration of the object.
vi – the initial velocity of the object.
vf – the final velocity of the object.

2. The four kinematic equations which describe an object's motion are:

3. Position Of Free Falling Object At Regular Time Intervals
The position of the free-falling object at regular time intervals, every 1 second, is shown. The fact that the distance which the ball travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward.

4. Velocity Of Free Falling Object At Regular Time Intervals
Assuming that the position of a free-falling ball dropped from a position of rest is shown every 1 second, the velocity of the ball will be shown to increase

5. Velocity Of Free Falling Object At Regular Time Intervals
Observe that the line on the graph is curved. A curved line on a position vs. time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration of g = 10 m/s/s (approximate value), you would expect that its position-time graph would be curved. A closer look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object, the initial small slope indicates a small initial velocity and the final large slope indicates a large final velocity. Last, but not least, the negative slope of the line indicates a negative (i.e., downward) velocity.

6. Velocity Of Free Falling Object At Regular Time Intervals
look at the velocity-time graph reveals that the object starts with a zero velocity (starts from rest) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object which is moving in the negative direction and speeding up is said to have a negative acceleration
This analysis of the slope on the graph is consistent with the motion of a free-falling object – an object moving with a constant acceleration of 10 m/s/s in the downward direction.

7. How Fast?
The velocity of a free-falling object which has been dropped from a position of rest is dependent upon the length of time for which it has fallen. The formula for determining the velocity of a falling object after a time of t seconds is:
vf = vi + (-g)t
where g is the acceleration of gravity (approximately -10 m/s/s on Earth; its exact value is m/s/s). The equation above can be used to calculate the velocity of the object after a given amount of time.

8. How FAST ? Example t = 6 s vf = (0 m/s) + (-10 m/s2) (6 s) = - 60 m/s

9. How Far?

10. How FAR ? Example
The NEGATIVE displacement, indicates that the object is falling DOWN