Kinematic equation

Question

I need help with a kinematic equation for an object in free fall. Define each variable

Answer 1

There are two kinematic equations:

v(t) = v(0) + at

x(t) = x(0) + v(0)t + at²/2

where

a is a constant acceleration.

It is important that acceleration be constant.

These equations are valid only for constant acceleration.

v(t) is velocity at a time t.

So, v(0) is "initial" velocity; that is, velocity of the object when we start counting time.

x(t) is position at a time t.

So, x(0) is "initial" position; that is. position of the object when we start counting time.

In the special case of free fall we have

a = g = -9.81 m/s²

I wrote the gravitational acceleration as negative because of the common convention that

upward direction is positive and downward is negative.

v(t) is vertical velocity, because that is the only direction of movement in a free fall.

Velocity will be negative when the object is falling down.

x(t) normally represents height above ground, or

could be height above any other reference level or you choice.

x(t) is positive when the object is above the chosen reference level,

and it is negative when it is below the reference level.

In the common situation when the reference level is the ground,

x(t) ≥ 0.

x(t) = 0 at time t when the object hits the ground.