Android: Using hardware sensor to detect the phone moving up and down

Question

I am creating an application where i need to monitor the phone's position, NOT orientation, but transition from one point to another. For exmample, let's say the phone begins at the height of a person's eyes, and i need to check if the phone has been lowered below the waist, let's say for this exmaple 1 meter. What hardware sensor should i use. What i was thinking was, to set the phone's position at the start at 0 for the z axis, and tell the user they have to start by holding the phone in front of their face. Then i would use a Linear Accelerometer to get the speed of the phone on the z axis the calculate using speed x time the distance. if the distance is >= 1meter, counter++;. I would also need to check to make sure that this calculation is done only if z is negative. Am i on the right track, any pointers out there. Thanks!