I'm sorry but to make it clearer do you mean to basically ask how prove that acceleration is related to velocity of an object that is moving in a fluid right?
So, that means that the object is traveling at a constant acceleration which technically means that there is an overall force acting on the object overcoming the resistive force of the fluid that enables it to accelerate. Hence, using the basic formula F=ma, that means that the object is accelerating due to a constant force acting on it.
And a = (v-u)/t
where u is the initial velocity at the start of a certain period of time and v is the final velocity at that period of time.
Acceleration is the rate of change of velocity so that is how it is related to the velocity? I hope I'm not lost. I'm scared I'm not making any sense here....