First be sure the machine is set for straight stitching, not zigzag, and that the needle position is centered over the hole in the plate. Try sewing without fabric and see if the needle still hits the plate after a few stitches. If it does, it has nothing to do with your moving the fabric too fast, and it might be time to call the sewing machine repair place. Otherwise, if your needle is hitting the sole plate, then it must be bending, which means the fabric is exerting sideways force on it. A heavier needle should help.