What is the application?
It seems an odd way to do it...
Imagine the following, sharp acceleration upto velocity V... over time (t)
Fine your accelerometer and time measurements will allow you calculate V.
However a very slow loss of V due to friction, aerodynamic drag etc will be difficult to measure with an accelerometer and thus V will become unreliable.

Maybe the application will explain this? Of course if it is space travel the V will be maintained...if it's a vehicle then the problem will be there.
Maybe it's an inertial guidance system for an arrow? _{<jumps up and down in excitement yowling wildly>}
Del

What the cat said (A GA to him in spite of his degenerate habit of ruining good whiskey by diluting it with cream).

In the general case, you can't do this. You would be integrating a signal and it's an indefinite integration. So, you need to provide a constant of integration. But that constant is a velocity so you need a speedometer to measure that. And if you already have a speedometer...

In particular cases, you can do it by a "gizmo". For example, you might build a little gear driven spinner whose rotational speed is proportional to the linear speed and then measure the acceleration of that and calculate velocity. But, you've just re-invented the speedometer except it's much more expensive and not as accurate.

Can you shed some light on why you need to do this and some detail on what your apparatus looks like?

I'm curious. What happens when you turn a corner? Won't that affect your "speed" reading? And once you reach a constant speed won't your accelerometer based system read zero, since accelerometers only react to changes in velocity?

Or, am I missing something?

What happens when you turn a corner....
good point.
With an accelerometer for each axis there's going to be some funky maths.
Del

See 'Inertial Navigation'.

Used by the U.S. Navy on subs with great accuracy.

Laser based accelerometers and laser gyros, doppler effect and phase relation of laser beam providing accuracies that are simply stunning.

MRH

I have designed a microwave based speedometer for use at an automotive factory in their research labs.

Basically its just a microwave transmitter and reciever package with the mixed signal as an output.

They use them as intruder alarms, based on the doppler shift caused by moving objects.

This doppler shift is an incredibly accurate way of measuring speed which is why the police use them to catch speeding cars....

All you need to do is buy a module - I have a few left over - and mount it pointing down at the road - any gravel or road bumps will reflect the signal back to the module giving you a doppler output which is directly related to speed....

Voila!!!! done!

Ok this is exactly the kind of thing i was serching for.Pretty neat idea.The basic idea for me was part of a bigger plan to measure wheel deterioration and slip over the period of time. Any other ideas in this regard are more than welcome.