The dot product of acceleration and velocity represent the power per unit mass, which means how quickly the object gaining the kinetic energy.
Recall that the power can be expressed as:
P = F . v
Where:
F = force
v = velocity
According to the 2nd Newton's law:
F = ma
where:
m = mass
a = acceleration
Divide the power formula by m:
P/m = F/m . v
P/m = a . v
Power here is the rate of change of kinetic energy, 1/2 m.v².
Hence, the product acceleration and velocity represent the power per unit mass, which means how quickly the object gaining the kinetic energy.
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