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That is, I think, typical of a treadmill (or any exercise machine powered with a motor) that has lost the ability to sense the speed the driving motor (and the belt) is running at.
This is signified by the sudden start at too fast a speed, followed by shutdown when (obviously enough) the system detects absolutely no speed indication from the speed sensor. After a small amount of time, a device with well-written digital firmware will know that it is not sensing the speed and it is the right thing to do to shut down completely.
Either you, or a repair-person, will need to look at the speed sensor, and adjust it, and/or test it with a meter, and hopefully by that means repair it. (Unless the board the sensor wires lead to is defective, or similar slightly rarer cases.)
What approach would you like to take, self-repair (hopefully - there is some hope of it being successful) or hired repair on-site or taken-into-a-shop ?