Drive shaft is going out
If your car shakes while accelerating check your motor mounts. Then check your transmission.
A car accelerates from to at a rate of How far does it travel while accelerating
You may have a broken engine or transmission mount.
When the car shakes n it on the correct its becsuse its out of timeing
If your car shakes while underway, your tires have worn incorrectly from misalignment. If it shakes while in park or not moving, your engine is misfiring.
Engine miss.
Could be mechanical, such as engine or tyranny mounts, worn ball joints or tie rods. Or fuel and timing problems.
Slow engine RPM is the main reason a car may be sluggish while accelerating. However, it also could be due to the oil.
dirty fuel line
if you car shakes when its fully stopped it may be the harmonic balancer, take it to a garage. is it shakes only when you are braking while stopping than have you brakes checked
A gas leak with the car sputtering while accelerating could be a hole in the vacuum hose that controls the flow of gasoline out of the tank. This type of leak is usually not caused by the fuel pump itself.
bad wheel bearings