I have a basic understanding of the reason why we look for derivative or integration in Physics, based on the water flow example, where integration is the process of accumulating the varying water flow rate "2x" , while we reverse to the water flow rate by differentiating " x squared " the integral of 2x. So I understand that in general we differentiate when we know the integration, ie the cumulative effect of a function but we want to know the function ? am I right ? given my limited knowledge I don't understand why we differentiate ( and also why twice ? ) in the picture attached. I will be very grateful for any help with basic terms. Thank you !