Several things should be checked for this such as wheel damage, tyres etc, but certainly on the C30 T5 any shaking on acceleration is often down to the driveshafts needing replacing. Do a search for driveshafts and hopefully a few posts on this will pop up. On the C30 many have tried aftermarket driveshafts without too much luck, so OEM Volvo ones seem to be the way forward but they are not cheap...!
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2010 C30 T5 – Now sadly gone but not forgotten 
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