How to find Particle Position at Time with velocity and friction?

Question

I have a Particle p.
A particle consists of a start position p0,an age t, a velocity v and a friction f

How can I find the position pt at an arbitrary t?

I currently have the formula

pt = p0 + (v*t), which works fine.

But I don't know how to corporate f into it.

f is a multiplier, that should reduce velocity per timestep: v' = v*f

I tried p0 + (v*t * (f/t)) but at time 0 it's a division by 0, and when t is high, pt converges to p0

What platform is this for? Ones Like Unity and UnrealEngine already have inbuilt methods for things like this? — akaBase, Oct 01 '21 at 23:50
This is more complicated than it might seem, and I'm not sure whether a closed-form solution exists. — DMGregory, Oct 02 '21 at 14:01
@DMGregory I see. Thanks. Is there a rough approximation (it doesnt have to be mathematically accurate, it's for visual purposes only) I can use? All I want is slow down the particles according to some parameter and I would like to keep the loop for the particles as tight as possible, without any expensive calculations. — Raildex, Oct 04 '21 at 05:48
See the bottom of that answer I linked, where I suggest such an approximation for short time steps. — DMGregory, Oct 04 '21 at 10:55

score 1 · Accepted Answer · answered Oct 02 '21 at 12:16

1

Maybe try this:

pt = p0 + v*t - 0.5ft^2

It's the physical equation for motion with constant deceleration, just make sure to stop it and save the position when v reaches 0:

Vfinal = V - f*t

So for V final = 0 you wanna stop it at t = v/f

answered Oct 02 '21 at 12:16

YepNope

1 Answers1