Calculating Calories burned from mass and acceleration

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I know force is equal to mass times acceleration. What I'm trying to do is find a formula that will calculate how many calories are burned using mass, acceleration and time.

For example, if I have a two pound object in my hand and I am shaking the object at 3 mph for 30 minutes, how many calories have I burned?

If anyone can provide a formula for this, it would be appreciated!

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Decide if you are shaking the object in a vertical path ( from low position to high and viceversa ) or on a horizontal plane. The two "path" require different energy.

Calculate the energy for that kind of movement ( mass, length of movement ).

Then sum how many movements you can do in 30 minutes.