1. Gravity & Free-Fall

2. Free-Fall
An object is said to be in free-fall whenever gravity is the only force acting on the object.
Typically this will be true when an object is
Falling downward from rest (v0 = 0)
Moving upward but slowing down after being thrown or launched upward
Moving downward and speeding up after being thrown or launched downward

3. Free-Fall
It turns out that when we actually drop different kinds of objects and allow them to free-fall, they all accelerate downward at the same rate:
We call this the acceleration due to gravity, and give it a special letter, g. This rate of acceleration is CONSTANT while the object remains in free-fall.

4. Free-Fall
Since any object in free-fall near the surface of the Earth has a near CONSTANT acceleration, “g”, we can modify each of the previously derived kinematics equations as follows when we apply them to an object in free-fall:
*Note that since the gravitational acceleration is always “downward” (toward the center of the Earth), we are essentially substituting –g for the acceleration a. In general, “g” itself will be considered POSITIVE, and the (-) sign will be part of the formula.

5. Free-Fall
Since any object in free-fall near the surface of the Earth has a near CONSTANT acceleration, “g”, we can modify each of the previously derived kinematics equations as follows when we apply them to an object in free-fall:
*Note that since the gravitational acceleration is always “downward” (toward the center of the Earth), we are essentially substituting –g for the acceleration a. In general, “g” itself will be considered POSITIVE, and the (-) sign will be part of the formula.

6. Free-Fall
Since any object in free-fall near the surface of the Earth has a near CONSTANT acceleration, “g”, we can modify each of the previously derived kinematics equations as follows when we apply them to an object in free-fall:
*Note that since the gravitational acceleration is always “downward” (toward the center of the Earth), we are essentially substituting –g for the acceleration a. In general, “g” itself will be considered POSITIVE, and the (-) sign will be part of the formula.

7. Free-Fall IMPORTANT NOTE:
Just because an object is accelerating the vertical dimension, does NOT necessarily mean it is in FREE-FALL.
If any forces other than gravity are acting on the object, we cannot assume that its vertical acceleration (ay) equals “-g”.

8. Free-Fall
In these cases, we must determine the vertical acceleration (ay) using Newton’s 2nd Law, which you will learn about in the next unit, and substitute that acceleration (ay) into our kinematics equations as follows:
*Note that since the vertical acceleration in general may be upward or downward, we leave the (+) as part of the formula, and substitute a POSITIVE VALUE for ay if the vertical acceleration is upward and a NEGATIVE value for ay if the vertical acceleration is downward.

9. Kinematics Equations Horizontally Accelerated Motion Vertically
Free-Fall
(ay = -g)
Velocity as a Function of Time
Displacement as a Function of Time
Velocity-Displacement Relationship