Hello,

 

A few times I've been stumbling across this equation on the net, but a quick search through my mechanics books didn't help much.

 

It states that for an object:

 

ds = v * dt + (a * dt^2) / 2

 

where ds is distance moved, dt is time, v is velocity, and a is acceleration.

I haven't been able to make any sense from it, and I haven't been able to make it work in an programs that I tested it in.

 

edit: I take it we all agree that ds = v * dt, and that's pretty much it? (given a constant velocity)

 

michael

Unless your saying [math]\frac{a}{2} dt[/math] is equal to zero, that equation is incorrect.

 

In other words, velocity is equal to zero. Otherwise Its wrong. I've never seen that equation before.

This equation gives you the position as a function of time assuming a constant acceleration. In the equation v is the initial velocity. If the acceleration is not zero then the velocity will not be constant. If the acceleration is zero (a=0) then the equation becomes that of an object moving at a constant velocity.

I've never seen that equation before.

 

I am sure you have seen this equation, better written in the form

[math]x=x_0 + v_0\Delta t + \frac 1 2 a\Delta t^2[/math]

My bad, I guess I have seen that equation before then Sorry, My Brains Been farting alot recently..

Ah, now I've figured out what it was about. The equasion was used (incorrectly, though) in a second order differentiation algorithm solving the n-body problem. It's also called the leapfrog method. You can read about it here: http://www.artcompsci.org/kali/pub/msa/ch18.html#leap_half_time (Scroll a bit down to equation # 89)