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.

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.