how to calculate a negative acceleration?

Question

I\'m implementing the scrolling behaviour of a touch screen UI but I\'m too tired in the moment to wrap my mind around some supposedly trivial piece of math:

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Answer 1

I will add a thought as well. Looks like you don't want a constant (negative) acceleration. That would result in an equation like:

v(t) = v(0) + a*t,

where a is the negative acceleration, t is the time, and v(t) is velocity at time t. This gives you:

v(t2) - v(t1) = a(t2-t1),

and that means that for a given Δt the velocity difference is equal to aΔt, a constant.

What you may be looking for is for a "friction" term, that depends upon the current velocity. Under that assumption, the rate of change of velocity is proportional to the current velocity:

d v(t) / d t = -b*v(t).

Solving the above is easy, and you get: v(t) = v(0) e^{−b t}.

Integrating this equation, we get x(t) = v(0)(1−e^{−b t}) / b, where x is the position. The position plot¹ for v(0) = 1, b = 0.1 looks like something you could use. Playing with the values of b, and adding a scale factor to the equation might be what you want to do.

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¹ http://www.wolframalpha.com/input/?i=plot+%281+-+1+e^%28-0.1+x%29+%29+%2F+0.1+for+x+%3D+0+to+100