The speed with which the transfer happens is roughly the speed of sound in the medium.
If the object striking the target, is moving faster than the speed of sound of the target, the energy remains behind the projectile, doing lateral damage; sonic energy boom that trails the projectile. This how they take out hardened tanks with high momentum rounds; very heavy metal bullet like depleted uranium, at high speeds. Uranium is about 19gm/cc while iron is 8gm/cc.
There is a toy on the market called "silly putty" that you can mold like putty. However, if you mold it into a ball and throw it against the ground or a wall, it will bounce back with almost perfect rebound; little loss of energy. It acts like a super ball.
An interesting secondary effect, not connected to compression energy; projectile or bounce, it connected to tensile strength and energyy. The silly putty will stretch like gum if you slowly pull it apart. But if you pull it fast with a jerk, it will shear at a smooth plane. It properties for compression and tension are speed; time dependent. If we had a wall of silly putty and softly toss a rock at it, the rock will stick into it. If we throw the same rock really fast at the silly putty wall, it will bounce back and hit us at about the same speed.
If you go slow enough the weakly held long polymers chains of the putty can slide past one another to move and compress like putty or stretch like bubble gum. But if you go faster, the weak chemical binding between the polymer chains, does not have time to side, so the silly putty will appear to harden, and will shear under tension or bounce under compression like a super ball. This is an example of a nonNewtonian material that behaves differently from most metals and ceramics.
Water is interesting in that something similar happens when you make water go faster and faster. Slow water feels soft, but as it goes faster and faster it start to act like a solid; pressure washer. The hydrogen bonding takes time to break, and if you go really faster the hydrogen bonds cannot move fast enough and liquid water acts more like ice. It can even be used like a saw through stone.
The Properties of Materials was my educational specialty.
Although not related, there is a simple home experiment one can do to experience an entropy change. The concept of entropy is often seen as nebulous, but proof is in the pudding; first hand experience. All you need a rubber band. Rubber is a polymer where all the polymer worms are cross linked with sulfur bridges.
In the first test, you take a room temperature rubber band and hold it to your lips. The lips are sensitive and can feel any subtle temperature change. If you stretch the rubber band, on your lips, you can feel it get warmer; exothermic. Next, keep the rubber band stretched for a few minute, until it cools back tor room temperature, while remaining stretched. Next, put it back to your lips and let it contract; you will feel it cool; endothermic.
The cross linking of the polymer molecules in rubber band, at rest are vibrating and taking up space. As we stretch the rubber band, the polymers are aligning with the tensile force adding order to the rubber band; entropy or complexity decreases with the release of heat. When we let the rubber band contract, the polymer molecules can assume a more expanded vibrational state increasing entropy; back to more disorder. An entropy increase adsorbs heat; get cooler.
a rubber band is designed to already be at maximum entropy, and any change that lower entropy; stretch or compression, will be resisted and if allowed to overcome, the rubber will return to its memory of maximized entropy; repeatable entropic state.