please look at this equation

[h4tt3n]

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

[Ragib]

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.

[m4rc]

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.

[D H]

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]

[Ragib]

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

[h4tt3n]

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)