1. The problem statement, all variables and given/known data (I'm learning all of this in German, so I apologize if something is translated incorrectly.) So last week we started calculus of variations, and I'm rather confused about how to approach the following problem: The fuel consumption of a vehicle per unit of time is expressed as follows: In which the vehicle travels a distance D in a given time T. v(t) is the speed of the vehicle (a, b are constants). The beginning condition is v(0)=0. For what v(t) is the fuel consumption minimal and compare this consumption with another v(t) contanting a constant acceleration. A tip is then given: Find the functional J[v] which reflects the fuel consumption and the functional for the condition. Take note that v(T) isn't given, but that the stationary J[v] implies a boundary condition of a(T) = 0. 2. Relevant equations Based on the problems we received last week, I assume y(t)+εη(t) is necessary for the minimization of this problem. 3. The attempt at a solution So I'm not sure how to determine the functional J(v) that reflects the fuel consumption, but I have assumed the velocity function is any sort of y(t)+εη(t) which fulfills the condition that df/dt = 0. (Which means it is extremal) Otherwise I'm pretty lost here guys. Thanks so much for the help!