# Figure out rate of change of speed for fixed distance

Say I have two points. I know the distance between those points. And let's say I have a bobbin that's starting at point A at a fixed speed of 100 jiggers/second

By point B, I want my bobbin to only be traveling 20 jiggers/second.

What equation can I use to figure out what rate of change of speed I would need to apply to my bobbin to slow it down to 20 jiggers/second?

How would I do it so that it eased into the new speed?

I apologize if this is poorly worded or an asininely easy question. I'm a game developer, and I'm not really sure how to ask this question in a Google-friendly fashion.

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Isn't a jigger a measure of volume, not distance? –  Ataraxia Jun 23 '13 at 15:35
So you want a constant acceleration, right? The answer will be in, say, $m/s^2$? –  dfeuer Jun 23 '13 at 15:36
Yes, exactly, $jiggers/sec^2$. At least that's what I figured. –  dclowd9901 Jun 23 '13 at 15:39

This is a basic kinematics problem, in which two things are known:

The distance between points: $d$

The initial and final velocities: $v_f=100$ j/s and $v_i=20$ j/s

To find the desired acceleration, use the equation:

$$v_f^2=v_i^2+2ad$$

Where $a$ is the acceleration.

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Thanks for the link and the answer! I'll read up on it some more. –  dclowd9901 Jun 23 '13 at 15:49
So, solving for $a$, it's looking like $\frac{v_{f}^2 - v_{i}^2}{2d} = a$, is that about right? –  dclowd9901 Jun 23 '13 at 15:58
@dclowd9901 Yes, that is exactly right. –  Ataraxia Jun 23 '13 at 16:12