Which equation correctly relates final velocity to work W and mass m for an object starting from rest?

• A. v = sqrt(2W/m)
• B. v = sqrt(W/(2m))
• C. v = sqrt(Wm/2)
• D. v = sqrt(W/m^2)

Answer: (A)

Think in terms of energy: the work done on an object translates into its kinetic energy. If the object starts from rest, its initial kinetic energy is zero, so the work W equals the final kinetic energy, which is (1/2) m v^2. Setting W = (1/2) m v^2 and solving for v gives v = sqrt(2W/m).

This also ties to the broader relation v^2 = v0^2 + 2W/m; with v0 = 0, it reduces to v^2 = 2W/m, hence v = sqrt(2W/m).

Check the other forms: they would imply different relationships between W, m, and v that don’t match the kinetic-energy expression, or mix units in ways that don’t yield velocity correctly. The correct expression naturally comes from equating work to kinetic energy for motion starting from rest.