42 minutes? The diameter of the earth is 7,918 miles. That is an average speed of over 11,000 mph.
He’s assuming there is a vacuum in the hole. You would not reach terminal velocity because there would be no air resistance.
You would accelerate all the way to the center, so you’d get moving pretty fast.
However, acceleration due to gravity would steadily decrease as you approach the center. Your momentum would carry you through the center, then you begin decelerating.
http://en.wikipedia.org/wiki/Schuler_tuning
It’s the same period as the period of a satellite orbiting the earth just above the surface.