jremington:
Only if you know the initial velocity, and can cancel the measured acceleration due to gravity.The latter is essentially impossible with consumer grade accelerometers/IMUs, as anyone who has tried quickly learns.
Yes, that is correct.
I was assuming that the swimmer started at zero initial velocity.
The OP implied that he had a three axis accelerometer, so it would be possible to measure horizontal acceleration in the direction of travel.
The measurement would become complicated when the swimmer went from being upright on dry land to being horizontal in the water as the axes get flipped around. Also the largest acceleration may be during this period if the swimmer dives into the pool.