The lesson to be learnt here is  that both approaches can work, just remember to never double count the work done!
 

4. Momentum

4.1 Conservation of Momentum

We recall Newton's Third Law: Every force has an equal and opposite reaction. From this law we are able to determine the conservation of momentum: the total momentum of a system stays constant.

4.2 Force as the time derivative of momentum

Now, thus far we have defined force as the product of mass and the acceleration, but we will now swap out to a more precise mathematical definition of force: the time derivative of momentum.