2 possible issues, warped brake disc, or failing steering dampner.
It must be the rear brakes at fault.
the brake rotors are warped. resurface or replace rotors. if the vehicle shakes without applying the brakes, check tire balance.
If the steering wheel shakes, but to car doesn't, when applying brakes - your front rotors are warped (if you have disc brakes)...if you have drum brakes, the drum could be cracked or the pads worn unevenly If the whole car shakes, and the steering wheel only seems to react to that, when applying brakes - see above statement, but apply to the rear end. If the whole car shakes, including the steering wheel - all four corners are bad, and you're an accident looking for a place to happen soon. In any case, go to your nearest service center ASAP.
Good question. You may have an antilock brake circuit that is not sensing the brakes correctly and improperly correcting. Anti lock pulses the brakes when you apply them. I don't know if this is perfected or not.
warped rotors(brakes)...most likely front ones
depends on when it shakes if it shakes when you put on the brakes-warped rotors otherwise it could be ball joints, steering joints, wheel bearings or even out of balance tires
check the rotors they could be warped
Shaking when accelerating and braking show a front end issue. Check the lug nuts to make sure your tires are bolted on tight. Check for play in front end components, like the wheel bearings and tie rod ends. While possibly causing the vibration, the front brakes usually only cause a shake when braking.
Contaminated fluid? Frozen calipers?
worn front end parts (steering or suspension) could cause a car to shake when appling the brakes.
This is usually a symptom of excessive run-out (warped) on front brake rotor or rotors.
Your rotors are warped. You need new brake pads and the rotors turned at a machine shop or replaced.