maybe the car need to be linged up n check the power steering.
During acceleration? I'm not sure. But when both idling and acceleration the engine's combustion can cause a lot of vibration in the steering wheel if you are in an older vehicle.
Steering wheel vibration when applying brakes is usually caused by warped disc brake rotors
This is probably due to worn brake rotors on the brakes, if there is no vibration when driving then this will be the cause.
A flat tire is one possibility
Out of alignment.......warped brake rotor......broken belt in a tire.....
Wheels are out of balance
Go to a garage, and get the wheel balancing checked out on the front wheels.
well... there are many different causes for vibrations. The most common cause for steering wheel vibration at high speed is poor wheel alignment.
A steering wheel that is padded with leather for comforment when driving
most of the time bad allignment or not balanced tires. You could also have a bent rim.
If the steering wheel is loose while driving the steering rack may be going bad. A bad steering rack leads to a lot of play on the actual wheel.