Assuming it is not driver error there are two possibilities.
Either the clutch is slipping under higher torque delivery and causing the vehicle to buck, or the transmission is damaged internally.
If it is a clutch issue it's only a matter of time until the clutch fails, but make sure there is no oil or brake fluid on the clutch disk - this will damage the new part as well.
The easiest way to tell if it is internal damage is to look for debris in the fluid - try draining the fluid through a coffee filter. A little metal shaving discharge is normal, but any larger particles indicate a problem.
Poor driver or bad transmission.
If it's an automatic, your transmission may be dying; if you drive a manual, you're probably letting the clutch out too fast.
That might be the sign of a transmission problem. My car used to jerk when I put it in reverse. But if you wait a couple seconds until it is completely in gear, I bet it won't jerk. Having it checked out with a mechanic maybe in your next oil change might be a good idea. Tip for checking your transmission: When you are driving 60mph, put your car in neutral - if your car rolls smoothly in neutral, there is no problem. If it shakes or does something weird, you wanna have it checked out. Reminder: Putting the car from FORWARD gear (not reverse) to Neutral while in motion in either automatic or manual gearbox will not damage the transmission.
You will feel a jerk from the engine / transmission when putting in gear. This can inturn damage the CV shafts.
Possibley, the Clutch sensor, or the transmission is going.
If the automatic transmission car jerks when accelerating and the dash does not indicate a gear, there is a problem with the transmission. Check the shift solenoid.
Check the mounting of the gear box, because the mounting of the gear box is like shock absorb.
You could have ignition problems if it is the engine causing the jerk.
If it's an automatic it's the transmission downshifting and choosing the correct gear.
could be failing transmission
Its normal for most manual cars the clutch is basically shifting gears in the engine but if you are accelrating shifting gears higher it could jerk a little bit so it can lock the gear and preset the engine to the desired gear Now if this is an automatic here you are not hitting the brake pedal fully Transmission fluid is low or empty Or it can be just old so it can jerk a bit to get into gear... however it is potentially bad for an automatic car because it has more parts and the thing it would do the most harm to is the gearbox.
If a car jerks forward while in the break position it is not the Automatic Break System but rather the transmission.