"Accelerates" means a change in velocity.

Now I don't need to have fun as the language police and say the only way the engine can accelerate is for it to run off and leave the car, but it would help to know if the RPM starts rising from a normal idle speed or if it's stable at a higher than normal RPM.

The list for higher RPM includes a stuck throttle cable/throttle body, sticky IAC (idle air control), and for an intermittent a vacuum leak that opens & closes as the engine moves - not uncommon particularly for a PCV hose.

 

The RPM rises on it's own at idle speed.
At parking the RPM rises even more than at idle.

 

I was trying to get more info. on what happens when to narrow down some suspects.

The general list above for ways extra air can get to the engine to increase RPM will have to suffice.

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In normal operation the RPM is high on start up, higher when it's colder.

That drops as the engine warms, eventually settling at a normal idle speed. If you happen to be driving already, you won't see normal idle until coming to a stop down the road.

Once it warms up and idle is normal, every action that affects idle speed is compensated for by the IAC. Put an automatic in gear, IAC needs to supply more air to prevent stalling. Even power steering use or high battery charging loads on the alternator are compensated for.

Witnessing these operations take place can let you know if the IAC is working properly, all without picking up a tool.

To see if the throttle body (TB) and the throttle cable are moving smoothly with no hangups you need to open the hood and operate them by hand (engine off) to check their physical operation.

Beyond those items, the next suspect for incorrect idle speed is a vacuum leak letting extra air enter the engine. Books can be written on that alone, beyond looking for simple faults like disconnected/broken hoses I'll leave that to Google for now.

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Trying to find out IF it settled to a normal idle speed at any time and THEN started to rev higher was part of attempting to diagnose from a distance. The more detail about what it does when the better.

Idle speed is the steady RPM an engine settles to with no throttle inputs.

"The RPM rises on it's own at idle speed." is a contradiction, so I can't tell from that if it idles high, settles to normal idle THEN it increases, starts rising after you take it out of gear, or what else it might be doing.

 

P.S. - My Bud amc49 here and a few others might phrase it a bit clearer.

"I've met the enemy and it is me"

"Can't fix an issue you can't describe"

Etc..

That is often considered harsh, but it's a truism. The first step in diagnosis is to confirm exactly what is happening, and how that varies from normal operation. The more detail that can be figured out for those differences, the closer you are to a good starting point for diagnosis.

Working with others at a distance make it even harder.

Not only do you need a clear picture of what is happening, but that needs to be communicated SO well that others can see it as if they were present. This often requires a message exchange, as someone responds with what they gather (or don't) from the first description.

Only when both parties confirm understanding can an accurate attempt be made to help in diagnosis. Often only suggestions can be made for further checks/possibilities, but sometimes the description is so useful as to point directly at a well known issue for a first check.

On your own, it's often necessary to gather more info. before even making an attempt at diagnosis. Intermittent issues are the worst, and all you can do is to plan ahead on what to check (if possible) when it occurs again or just try to note more details of EXACTLY what conditions exist when the problem is seen.

Making guesses and tossing parts at a problem seldom helps until a theory that can be tested for the possible cause is figured out.

In this case the initial theory is limited to what items can make the engine speed increase, then check them all, since there is limited info. on the details of the occurrence.

 

X2. A second post is wasted time (ours at least) if OP doesn't say any more than first post did.............

Add to list of things that can do it some goofball messing with the TB butterfly set screw, they think they can 'adjust the idle speed' with that.................that ceased in '86 but try telling neanderthals that.

 

The idle speed from a standstill idling at 700 - 800 RPM will rise to about 3200 RPM in 3 seconds without touching any controls all by itself and will not decrease until you drag the RPM down with the brakes and clutch. It will stay idling at 800 RPM for about 5 seconds and then starts the repetitive cycle again. It used to happen more when it was cold but now it doesn't matter, the RPM will increase at random 3-4 times you drive it about 5 miles. Engine is in a 2002 focus with the dual Over Head Cam and black plastic valve cover with the spark plugs between them.