This might work for you.
On the Logo layer, set keyframes for Position for the basic collision.
For the Dust:
Make a duplicate of your logo layer (Ctrl D). On the top logo layer, apply Scatter, amount 0 at impact, then one frame later (Page Down), amount = 50 (to taste) (uncheck Randomize Every Layer). this is the dust. Now set keyframes for the dust falling, if you want it farther below the logo, or if you want it to fall to the base, disconnect the x and y of Scale (S) by clicking the “Constrain Proportions” symbol (looks like an infinity symbol), then drop the Y Scale from 100 to something like 4 (looks like the dust is lying on the floor then) over time to let the dust settle. You should move the anchor point of the copy to the bottom of that dup logo layer with the Pan Behind tool, this lets the dust settle downward. There are probably Particle solutions to the dust, maybe somene else will chime in.
On the lower logo, you could add this Marker triggering expression to Scale so that on impact, you get a little shudder of the logo. Copy the expression, then Alt Click the Scale Stopwatch, then Paste:
n = 0;
if (marker.numKeys > 0){
n = marker.nearestKey(time).index;
if (marker.key(n).time > time){
n–;
}
}
if (n == 0){
value;
}else{
maxDev = 5; // max deviation in pixels
spd = 40; //speed of oscillation
decay = 10.0; //how fast it slows down
t = time – marker.key(n).time ;
x = scale[0] + maxDev*Math.sin(spd*t)/Math.exp(decay*t);
y = scale[0]*scale[1]/x;
[x,y]
}
You need to add a Marker (* on the numeric pad) and that will trigger the expression. You’ll need to move the anchor Point, again with the pan behind tool, this time move it to the point of impact.
This is a hack of several Dan expressions. Change the maxDev,spd, and decay to taste, it gets rubbery real fast.