It's possible you have a bad wheel bearing, or, if it's a front wheel drive car, bad CV joints are also a possibility.
The year, make model and engine info would be helpful.
A car accelerates from to at a rate of How far does it travel while accelerating
sounds like a cv joint
why does my car pull to the right when accelerating and pulles to the left when easy off acceleration
If it just does it a little its probably torque steer. Its common in fwd vehicles.
Your brakes need replacing. The right hand side is probably worn to the metal disc.
Drive shaft is going out
You rolled over a batch of chewing gum which then had gravel stuck to it.
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
I just fixed this problem on my own car, and it was that the rubber part on both the right side motor mounts was broken, so it would shake and make a loud noise when in drive and especially while accelerating. Depending on your car, you might be able to check for yourself, at least on a top side mount.
No, the right side of the car is the passenger's side.
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.