Free fall equations 

The free fall equations are shown below for free falling objects.

In order for you to understand how we found these equations, it is important  to understand speed, acceleration, free fall, and acceleration due to gravity.

We have already talked about speed and acceleration

What is free fall? Whenever an object is dropped in the air from a certain height, this object is falling. The object is not experiencing free fall just yet. Why do we say so?  If you drop a feather and a piece of rock from the second floor, the rock will accelerate faster and get to the ground faster.

This happens because of air resistance. However, if you put the feather and the rock in a tube and remove the air with a vacuum pump, the feather and the rock  will have the same acceleration.


Objects experience free fall when there is no air resistance or when air resistance is negligible.

Now, it makes sense why we say free fall equations.

It is because they are found when objects are affected only by gravity but air resistance is negligible. 

Now, let us try to find the acceleration due to gravity only.

If you could drop a rock from the 10th floor and equip the rock with a speedometer that can record the instantaneous speed during each second, you will end up with the following data:

  Elapsed time in second(s)









Instantaneous speed in m/s









Remember that the formula to find the acceleration is

acceleration =
change in speed / time interval

acceleration =
40 - 30 / 4 - 3

acceleration =
10 m/s / 1 s

The acceleration is 10 m / s2

10 m / s2 is read 10 meters per second squared

Where did the exponent of 2 come from? A little bit of math may help

Still don't get it ? Visit dividing fractions

Since the acceleration is due to gravity, we use g and write g = 10 m / s2. g is not the same everywhere in this world.
more accurately, g = 9.8 m / s2
From the data we see that 20 = 10 m/s × 2 or 50 = 10 m/s × 5

In general, v = g × t

If the object is thrown with an initial velocity, the equation is

v = v0 + g × t      v0 is the initial velocity

When an object is thrown upward or straight up with an initial velocity, the object is still subject to gravity. Moreover, the speed will decrease until it reaches 0.

Therefore, the speed will decrease by 10 m/s each second.

When the highest point is reached and the speed is 0, it will start going down and increase by 10 m/s each second.

We have found two free fall equations so far dealing with how fast. What about how far the object moves?

Free fall equations: How far ?

Recall that average speed =
total distance / total time

total distance = average speed × total time

How do we find the average speed? Using our data, what is the average speed from 0 to 10 m /s ?

For any object moving in a straight path with constant acceleration, we find the average speed the same way we find the average of two numbers. So, the average speed between 0 and 10 m /s is

Average speed =
0 + 10 m / s / 2

Average speed  = 5 m / s

In general, average speed =
initial speed + final speed / 2

To get the speed at any instant, we can use v = g × t. Thus, the same formula can be used to get the final speed.
average speed =
0 + g × t / 2

average speed =
g × t / 2

Multiply the average speed by the total time or t

g × t × t / 2

d =
g × t2 / 2
If there is an initial velocity,

d = v0 × t +
g × t2 / 2

Summary of all free fall equations

v = g × t

v = v0 + g × t      v0 is the initial velocity

d =
g × t2 / 2

d = v0 × t +
g × t2 / 2

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