- #1
etotheipi
Sorry for the silly question! If we start of with the relationship $$\int_{x_{1}}^{x_{2}} F dx = KE_{2} - KE_{1}$$ and then state that at position x1 the velocity (and hence also kinetic energy) of the particle is 0, and at x2 its velocity is v, is it sloppy or valid to write the integral representing the work done to increase the velocity from 0 to v as $$\int_{0}^{v} F dx = KE_{2}$$ or is it necessary to change the integrand to something like the following $$\int_{0}^{v} F \frac{dx}{dv} dv = KE_{2}$$