The work done from time t to time t + Δ t along the path C is defined as the line integral ∫ ∫ C F ⋅ ⋅ d x = ∫ ∫ t t + Δ Δ t F ⋅ ⋅ v ( t ) d t , so the fundamental theorem of calculus has that power is given by F ( t ) ⋅ ⋅ v ( t ) = m a ( t ) ⋅ ⋅ v ( t ) = τ τ ( t ) ⋅ ⋅ ω ω ( t ) .