An arrow leaves a bow at 25.0 m/s, and if the average force is doubled while keeping other factors constant, the new speed can be calculated using the work-energy principle. The first case uses the equation Fd = 1/2mv^2 to derive the initial speed. In the second case, doubling the force results in a final speed of 35.4 m/s. The discussion highlights the relationship between work done and kinetic energy, emphasizing that all work contributes to the arrow's kinetic energy. The conversation also touches on the difference between work-energy equations and kinematic equations.