I turned my car on first thing this morning and stepped out into the driveway get the newspaper while the car was in park. I then noticed that the car slightly lurched forward when the ICE turned on. Is it normal for the car to move a bit when the engine turns on.
Yes, it is just taking up the play between the parking pawl and the gears. There are several threads on this if you would like to search.
It is normal. It doesn't lurch but rolls or rocks a little foward untill the trans catches. If you use your parking brake this wont happen.
It might move 5-10cm max - not more. It is similar to what happens the same when you turn off the Prius without the parking brake, set P and then release the brake. For the trans to catch the P ring gear, will let the car move 5-10cm. If the car is parked on a slight backward incline and then the ICE turns on, the surge of torque will push the car until the P ring will stop it. Likely you will not get the same if the car is parked on a slight downward slope. In any case - nothing wrong or to worry about.
My Gen II does it. Not very often, since I usually have my foot on the brake, but it does happen. As for distance, it moves about three inches. Tom
The gen2 probably moves more than the gen3 because the gen2 is chain driven and has some slack in the chain witch is taken up when the parking brake is not applied.