Coast in Neutral + brake to slow down = HUGE SLAM?

I've noticed some interesting (at best) behavior on my 2002 Grand Am SE, 2.2L ECOTEC 4-cyl engine when coasting in neutral.
I recently moved into a house in a semi-ruralish, not-yet-developed (and
hope it stays that way) area with extremely little traffic, at the bottom of a hill. Driving home, I get off the main highway, which runs along the top of this hill. I discovered that if I put the car in neutral, I can just coast this way with the momentum keeping me at about 35 MPH (which happens to be the speed limit), having only to apply the brakes lightly at the end when it's time to pull in and park.
However, I noticed that frequently, but not all the time, the car will slow down smoothly as I apply the brake, only to LURCH forward HARD right at the moment the speed of the car drops below 10 MPH. It feels a lot like a 100-pound weight or so has suddenly shifted forward in the engine compartment and hit the front of the frame, stopping hard. However the car will never do this if I leave the gear in Drive and similarly coast (though I then find that I have to tap the brake on occasion to keep me at or below 35 MPH).
I had thought it might be something peculiar with the car, perhaps faulty engine mounts, but lo and behold, I discovered that my 2004 Chevy Cavalier, with the same 2.2L Ecotec engine (but I don't think it's the same transmission, not sure) exhibits the EXACT same behavior.
Also I recently had the opportunity to rent a 2005 Chevy Trailblazer, and for grins, I tried the coast with it. It did NOT lurch when I coasted in neutral. It has the Vortec 4200 Inline 6 engine, though, and is signifcantly heavier.
Anyone know what's causing the lurch? The cars don't seem to be any worse for wear, but I've stopped doing the Neutral coast, just in case.
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I got a hunch it's a brake thing. You're on you brak more when in gear, but only touch up at about 10mph when in neutral. Both your cars can't have loose calipers though. Try coasting right by without hitting the brake. Or try riding the brake slightly from the top like when in drive. Hey, maybe your seats are loose.
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Professor wrote:

Actually I have tried this as well to rule out the brakes. The car still lurches/slams forward as it approaches 10MPH.
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Isaiah Beard wrote:

Does the car have anti-lock brakes? My car sometimes has a pulseing at 10 m.p.h. and this feels as if the brakes "let go"
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Terry wrote:

The Grand Am does, but the Cavalier does not. Also the Grand Am has traction control, but not the Cavalier. I just find it odd that the two cars would do the same thing. The only common thing between the two of them is they're both FWD, and they have the same type of engine.
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Isaiah Beard wrote:

Hi...
Wondering if they were in overdrive, and just coasting, if that isn't the point that the convertors unlocked ?
Ken
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Ken Weitzel wrote:

Well see, taht's the thing. This only happens when the car coasts in neutral. When I coast downhill in overdrive, it's smooth all the way to the end.
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You aren't generating enough vacuum at idle to overcome the loss in the brake booster. Ala no power brakes.

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Woody wrote:

Vacuum is high at idle, low on acceleration <sp>, and highest on coasting in gear (engine braking). It's probably the converter clutch releasing. Coasting in N is something most people don't do, and possibly the tranny /computer doesn't know how to properly deal with it.. $.02
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