A vehicle should not accelerate by itself unless you press on the gas pedal which then moves the throttle cable.
However sometimes a vehicle may seem like it's accelerating by itself because of a faulty Idle Air Control Module that can be messing with the vehicles computer and allowing the engine to get more fuel or air which then makes the vehicle accelerate some without pressing the gas pedal.
I would have that idle air control module checked to see if it's the problem and if not then make sure nothing is pressing up against the gas pedal such as a heavy floor mat or something else that could roll into the gas pedal and cause it to accelerate.
Some vehicles will idle at a high RPM when you first start the engine and then after a few minutes it goes back to the normal RPM which is normal for some vehicles.
The Idle Air Control Valve could be faulty as well and need replaced because it could be allowing too much air into the throttle body like it would when you press the gas pedal.
When you press the gas pedal the butterfly on the throttle body opens wider which allows more air into the engine which then causes the engine to speed up.
Something could also be moving the accelerate a bit when it first starts up and may not be letting the RPM go down.
I would have a mechanic check the vehicle out before it gets out of controls and causes a crash.