<Dd> d W = d W d x → ⋅ d x → = F → ⋅ d x →, so P = d W d t = d W d x → ⋅ d x → d t = F → ⋅ v →, (\ displaystyle (\ text (d)) W \, = \, (\ frac ((\ text (d)) W) ((\ text (d)) (\ vec (x)))) \, \ cdot \, (\ text (d)) (\ vec (x)) \, = \, (\ vec (F)) \, \ cdot \, (\ text (d)) (\ vec (x)), \ qquad (\ text (so)) \ quad P \, = \, (\ frac ((\ text (d)) W) ((\ text (d)) t)) \, = \, (\ frac ((\ text (d)) W) ((\ text (d)) (\ vec (x)))) \, \ cdot \, (\ frac ((\ text (d)) (\ vec (x))) ((\ text (d)) t)) \, = \, (\ vec (F)) \, \ cdot \, (\ vec (v)),) </Dd> <P> with v → = d x → / d t (\ displaystyle ((\ vec (v)) (\ text ()) = (\ text (d)) (\ vec (x)) / (\ text (d)) t)) the velocity . </P> <P> Instead of a force, often the mathematically related concept of a potential energy field can be used for convenience . For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location . Restating mathematically the definition of energy (via the definition of work), a potential scalar field U (r →) (\ displaystyle \ scriptstyle (U ((\ vec (r))))) is defined as that field whose gradient is equal and opposite to the force produced at every point: </P> <Dl> <Dd> F → = − ∇ → U . (\ displaystyle (\ vec (F)) = - (\ vec (\ nabla)) U .) </Dd> </Dl>

Explain the concept of force and work with everyday examples