Depending on the make and model it could be a number of things, but the first thing I would suspect would be a clogged throttle body. Your engine requires air and gasoline to run and you might not be getting enough air into the system to get it going. You can remove the throttle body which is on top of the intake manifold usually and clean it. I would also change your spark plugs and add a fuel system cleaner for good measure. However, with it having trouble when being at a stop, I would guess the problem is air.
Lack of propulsion.
No, when anything is slowing down it is decelerating.
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.
Could be just in need of a tune up.
Most likely a dirty fuel filter or Bad Ignition Timing.
You may have a broken engine or transmission mount.
A car that hesitates or stumbles when accelerating can have dozens of different problems. Have a knowledgeable person look at it or post a question detailing all symptoms, trouble codes etc.
You need to check the throttle positioning sensor.
noise and jolting is present whilst car is idolling and accelerating
Frame of reference is the measurement or observation that tells you that a car is accelerating. It uses the second law of motion to tell you rather or not the car is accelerating.
The first thing is the oxygen censor could be the issue. There could also be a problem with the fuel pump.
The car is accelerating quickly as it speeds down the highway.