A block of mass 2 kg , initially at rest, is pulled by a force such that the power delivered by the net force is constant at 9 W . The net work done on the block by the time it has moved a distance of 16 m is

Step-by-step solution

The power delivered by the net force is given as constant P = 9 W . We know that power P = Fv = m a v = m v dv dt . Using the chain rule, dv dt = v dv dx , so we can write: P = m v^2 dv dx Separating the variables and integrating from x = 0 to x = 16 m and v = 0 to v = v_f : ₀^ v_f m v^2 dv = ₀^x P dx m v_f^3 3 = P x Substitute the given values ( m = 2 kg , P = 9 W , x = 16 m ): 2 v_f^3 3 = 9 16 2 v_f^3 3 = 144 v_f^3 = 144 3 2 = 216 Taking the cube root, we get the final velocity: v_f = 6 m/s According to the work-