Who made the uniform accelerated motion's ecuation (X-X0 =V0t+[at^2]/2)?

Question

Everything you know about who made the ecuation or proved it experimentaly will be helpful, thanks

Answer 1

Galileo was the first person to understand accelerated motion fairly fully. He experimented with balls and circular cylinders rolling down straight, inclined planes, balls rolling in curved bowls, and even balls rolling down shapes that were accurately cycloidal. He also learned much from experimenting with pendulums.

He obtained all the simple kinematical relationships that we use so often today, connecting constant acceleration, speed, and distance travelled. He actually PROVED a remarkable result that he found experimentally, namely that if you slide a bead down a smooth wire from the top point of a vertical circle, it will reach ANY point on that circle in EXACTLY the same time that it takes to FALL along the vertical diameter.

Another remarkable thing he noticed, though I don't know whether he PROVED it, was this: By putting two side-by-side cycloidal runways or tracks next to one another, he found that two balls placed at very different heights on those tracks, and let go, would arrive at the lowest points on their tracks AT EXACTLY THE SAME TIME!

(By doing this, he was in a way anticipating Newton's famous answer to Bernouili's challenge problem of the Brachistochrone - the descent curve of shortest time.)

The remarkable thing is that while WE would probably need to employ Calculus to solve all these problems, Galileo solved them by simpler (if perhaps more ad hoc) methods, before the Calculus was discovered!

Live long and prosper.

Answer 2

The equation you talk about is derived using Calculus. I would guess that it is likely the work of Issac Newton. Acceleration is defined as the time derivative of velocity, velocity is the time derivative of position. If we have a constant acceleration a, we can find the velocity at any given time t, by taking the integral (Note: I am using Int{ } to symbolize integration):

Int{a dt} from 0 to t

This gives us an expression for velocity with v0 being the velocity at time t =0 :

v = at + v0

We can than integrate this to find position as a function of time, where x0 is the position at time t = 0:

Int{at + v0 dt} from 0 to t

1/2 at^2 + v0t + x0 = x

This is the the equation you are looking for.