Consider this case: A ball is allowed to fall freely with a constant acceleration of 10 m/s^2. What will its speed be after travelling a distance of 10 m? We get that: v[initial] = 0 m/s d = -5 m (downward direction is taken as negative) a = -10 m/s^2 To find v[final], we will use the formula d = (v[final]^2-v[initial]^2) / (2a) Rearranging, we will get: v[final]^2 = 2ad + v[initial]^2 By plugging the numbers, we will get: v[final]^2 = 100 m^2/s^2 By mathematics, there are 2 solutions to this problem, that is v[initial] = +10 m/s and v[initial] = -10 m/s. I can only think of the situation where the ball has a downward velocity. Is the other answer (the one with +10 m/s velocity) possible/does it has a physical reality? If so, can anyone explain the situation? Thanks a lot!