Calculating Work Done by a Variable Force via Dot Product Integration
Consider a particle moving along a path defined by the vector function \(r(x) = (x, x^2)\), where \(x\) is in meters and varies from 0 to 2. The particle is subjected to a variable force given by \(F(x) = (2x, 3)\) Newtons. (a) Express the force function as a vector function of \(x\). (b) Calculate […]