Q: Jerking reaction when accelerating

What you are describing sounds like a dirty or faulty mass air flow sensor or potentially a bad camshaft position sensor. The mass air flow sensor monitors air intake as it is mixed with fuel prior to being injected into the motor. This sensor relays vital information to the ECM which uses this to make adjustments to fuel supply to the motor. A dirty or faulty sensor can cause an imbalanced air/fuel load to be supplied to the motor which results in an over fueling or under fueling situation depending on the conditions. This type of inconsistent fuel supply to the motor may cause a hesitation, loss of power, a jerking reaction, potentially a bit of black exhaust smoke and typically a strong smell of fuel when this sensor is malfunctioning.

The camshaft position sensor measures the rotational position of the camshaft and transmits that information to the engine control computer. To determine which cylinder is in its power stroke, your car’s computer monitors the rotating position of the camshaft relative to the crankshaft position using a camshaft position (CMP) sensor. It uses this information to adjust the spark timing and the operation of the fuel injectors. Thus, the CMP sensor affects fuel economy, emissions control, and engine efficiency. The two most common camshaft sensors you’ll see are the magnetic and Hall-effect types. Both transmit a voltage signal to an electronic control module or to the car’s computer. The magnetic type produces its own AC (alternate current) signal (a sine wave), and you can identify it by its two wires. The Hall-effect type uses an external power source to produce a digital signal (a "square wave," on-or-off) and has three wires. Depending on the specific model of your car, your engine may have one or more cam sensors. When the camshaft sensor fails, you may experience the car jerking while losing power or the car may struggle to move faster than ~35-40 mph. The engine may also stall intermittently, produce poor performance, hard starting, surging or fail to produce an ignition spark. I would suggest having an expert from YourMechanic come to your location to diagnose and inspect your vehicle.