Declaration of control

I need help in a Math logic issue. Let say I have an object that can be manipulate (move) by user. After the user moved the object I would like the object to continue moving and decelerate to a stop.

Example, when a user move an object from point A to B with 开发者_Go百科a total distance of 100pixel in X axis, after user release a finger, I want to let the object continue moving and decelerate to a stop from point B to point C.

So how can I calculate the new distance of point C if I set the time for it to decelerate and stop in 2sec?

Thank you!

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d = ½at² + v_it + d₀

d₀ is the point at which the user "let go". Calculate v_i from the motion before letting go. Set a to something negative; you'll have to fiddle with this to get it to feel right. Increment t from 0 through 2. d is where the object will end up. Remember that a and v_i are vectors pointing in opposite directions, and that d₀ and d are points.

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If the acceleration, a, is constant you can use the formula:

d = ½at²

With t = 2s you get d = 2a.

The acceleration is enough to accelerate to v in 2s, so a = v/2.

You get:

d = v

So if v= 100 pixels per second, the object should continue 100 pixels if it stops in 2 seconds under constant deceleration.

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If all you want is the distance from B to C, that's easy. If the object went a distance N pixels (say 100) from A to B in k seconds, then the distance from B to C will be N/k.

If you want the location of C, so that A, B and C are integers on the x-axis, C = B+(B-A)/k.

If you want to animate the motion, so that you can update the position x at every time step dt (say 0.1 seconds), then start (at B) with v=N/k, and at each step,

x += v * dt
v -= N * dt/(2 * k)

(Be sure to use floats, not integers, or the round-off error will ruin the effect.)