Rattling under acceleration is most often caused by your exhaust system. Check your heat shield for the catalytic converter or muffler. It may have come loose. Also, check the converter itself to see if some of the honeycomb inside has broken.
bad transfer case
Rattling under the hood can be something easy to fix to something bad. It could be loose bolts, bearings, pulleys, or it could be interior in the motor.
Something is out of balance, maybe the water pump is on its way out.
Worn Ball Joint
if its a front wheel drive vehicle then it could be the axels
bad wheel bearing may cause it
I would have your exaust pipe looked at, it might be loose, or might even be missing a bracket.
an air leak in your intake will cause the engine to rattle. Protege's intake hoses are prone to cracking.
It may be your catalytic converter. Ours did the same thing with an automatic transmission. We sometimes thought it was the transmission, then we received a recall on the converter. Took it in to be replaced, and no more rattling.
I'd like to know too! Mine does the same thing - it makes a rattling noise upon startup that goes away after 30 seconds or so and isn't present while driving or idling.
Could be a worn out shock or wheel bearings. Is it 4 wheel drive?
It could just be the heat shield on the under side of the catalytic converter.