Secondary Action

Loosely attached parts keep moving or trail behind after the main body stops or starts, so parts do not all move and stop together.

This is for a motion graphics video. Animate [scene] with "Follow Through and Overlapping Action" (also called drag or lag): the loosely attached parts trail behind when the main body sets off, and keep going, swing past and settle after it has stopped.
The parts must not all move and stop together. They are passive — pulled along by the body — unlike a secondary action, which is a small separate gesture playing alongside the main one.
Fit the move and the settling into [duration], and let longer or lighter parts lag further and take longer to come to rest.

One or two in-between frames distort or duplicate the subject along its path to fake motion blur during a very fast move.

This is for a motion graphics video. Use a "Smear Frame" (also called a smear or an elongated in-between) for the fast move in [scene]: for just a frame or two in the middle of the move, stretch the subject along its path so that it bridges the gap between the two positions.
The shape itself is redrawn — stretched, repeated as multiples, or trailed by motion lines — rather than blurred the way a camera would blur it, and the frames before and after stay sharp and undistorted.
Keep the whole move inside [duration] and very quick, so the smear is felt as speed rather than noticed as a shape.

Physics-driven motion that overshoots and oscillates around the target before resting; behavior comes from stiffness, damping and mass rather than a fixed curve.

This is for a motion graphics video. Drive the move in [scene] with a "Spring" (also called a spring animation or damped spring): a simulated spring pulls the object to its target, so it picks up speed from rest, runs past the target and swings around it before resting.
The motion should come from stiffness, damping and mass rather than a fixed curve — lower the damping for more swings, or raise it until the object settles with no overshoot at all.
Let it come to rest within [duration], and keep the same spring settings on every element so they feel like one material.

The object compresses and elongates while keeping its volume, conveying weight and flexibility.

This is for a motion graphics video. Animate [scene] with "Squash and Stretch": the object flattens when it lands or is hit, and elongates along its direction of travel while it moves fast.
Keep its volume constant — when it gets wider it must get shorter, and the reverse — and tie every change of shape to the movement, so it reads as weight and flexibility rather than a rubber-band wobble played on the spot.
Fit the action into [duration], and deform it a lot for something soft and only slightly for something stiff.