Question

HOW TO DERIVE FREE FALL EQUATION/

Answer 1

Derivation of the Freefall Equation

We begin by considering an object dropped from a height. Its initial velocity is zero. We'll let downward motion define the positive direction. We begin with the distance formula, and note that the velocity in that equation is the average velocity. Realize that the average velocity of a falling object (with constant acceleration) is just the final velocity plus the initial, divided by 2:

freefall derivation equation 1

Now use the definition of acceleration (here we'll use the acceleration of gravity, g = 9.8 ms-2) and the special fact in this problem that the initial velocity was zero, to get:

freefall derivation equation 2

Finally, we put these two results together, substituting gt for vf:

freefall derivation equation 3

... to get the freefall equation:

freefall equation