Is it possible to measure the velocity of a Unmanned Aerial Vehicle using only accelerometer? Our project is about dropping a payload from a UAV on the specified area. We are using an accelerometer (connected to the Arduino board) to measure the velocity of the plane (assuming the initial velocity to be zero). Is it possible to accurately measure the velocity of a plane moving in the air for a time t? Will this method be feasible?
Not with any measure of accuracy, no.

You're basically asking about Dead Reckoning which is problematical at best - and when doing it with just a low-grade accelerometer it can't be anything more than a rough "It's moving quick" or "it's moving slower now" accuracy.