A car shudders while accelerating when shocks are bad, tires are inflated improperly or tie road and suspension elements are starting to fail. These conditions are easy to test and exclude certain factors depending on how the vehicle reacts to bumps and bouncing. Try jumping up and down on the rear or front bumper of a car to test its integrity.
Shuddering indicates that there is an issue with the infrastructure of a vehicle. This type of problem relates to anything attached to the body of the car. Problems of this kind require that owners are aware that issues occur in the extremities of a vehicle in terms of tires, bumpers, paneling and other things that are bolted or suspended from the frame of the automobile.
It is easy to test which of these issues is the likely cause of shuddering. Standing on a bumper and bobbing up and down gives and bounces back in a normal car. A vehicle that does not provide much give or bounce bears damaged tie rods, shocks, tires or undercarriage issues. Anything besides these problems is indicated by watching the action of the engine or providing feedback from engine and emission readouts that are unique to the various functions of the vehicle.