Using the following equations I will show that v=gt

1) First lets establish our equations:

F = ma

a = v/t

v = d/t

where ‘F’ is force, ‘m’ is mass, ‘a’ is acceleration, and ‘d’ is distance

2) Lets look at the units of measurement

substituting the units of measurement for each variable, F = ma becomes

N = (g)*(m/s^2)

where ‘N’ is newtons, ‘g’ is grams, ‘m’ is meters, and ‘s’ is seconds

Similarily a = v/t becomes:

m/s^2 = (m/s) / s

In addition, v = d/t in units is:

m/s = m / s

3) Evaluate ‘g’

gravity is equal to 9.81 m/s^2

the units of m/s^2 indicates that gravity is a quantity of acceleration, such as given in F=ma or a=v/t

4) Substitute units to validify v=gt

v=gt in units of measurement is:

m/s = (m/s^2)*(s)

Sure enough, the ‘s’ from ‘t’ cancels out one of the ‘s’ in m/s^2 giving us units of m/s, which is the correct units for velocity.

5) What does the equation actually mean?

When you have an object that is dropped vertically (90 degrees to the horizontal) and begins at rest (0 m/s), the force of gravity pulls on the object so that it will gain speed at a rate of 9.81 m/s^2 until it’s descent is broken by the ground (aka the horizontal).

I believe it was Galileo who proved that objects fall at the same rate regardless of mass. This is the reason that a 10kg ball and a 1kg ball dropped from the same height will hit the ground at the same time, wind resistance negligible. By wind resistance neglibile, I refer to reason why a 70kg parachuter with a deployed chute descends at a slower rate than a 70kg parachuter without a depolyed chute. The chute when deployed catches air resistance which creates an upwardly force to counteract the downward force of gravity (F=ma, F=70kg*9.81m/s^2, F=686.7 N).

The actual equation of v=gt is useful if you need calculate at what velocity is an object after ‘t’ seconds of having been released from rest (0 m/s) from an arbitrary height and without any other force other than the force of gravity (meaning the item was dropped, not thrown).

For instance, if I told you there was a 2kg object dropped from a building 100 meters high, what is its velocity after 3 seconds, you’d be able to calculate

v = 9.81*3

v = 29.43 m/s

if you wanted to take it one step further, you could find how many meters the item fell after 3 seconds.

d = gt^2

d = 9.81*9

d = 88.29 meters

or even 1 step further to utilize all the information given, what is the force due to gravity of the falling object

F=ma

F = 2kg*9.81

F = 19.62 N