Which expression represents Newton's second law in vector form?

Which expression represents Newton's second law in vector form?

• A. F_net = m g.
• B. F_net = m a.
• C. a = F_net / m^2.
• D. W = F_net a.

Answer: (B)

Newton's second law in vector form says that the net force acting on an object is equal to its mass times its acceleration, with both sides as vectors: F_net = m a. Here mass is a scalar that scales the acceleration vector, so the acceleration points in the same direction as the net force. The magnitude of acceleration is F_net divided by m. This form is the general statement of the law. A specific case like F_net = m g would only apply when gravity is the only force acting, not in general. The idea that a = F_net / m^2 is incorrect because the mass should be in the denominator to first power, not squared. And work is not obtained by multiplying force by acceleration, so W = F_net a is not correct either. A valid rearrangement is a = F_net / m, which is equivalent to the vector form.

Newton's second law in vector form says that the net force acting on an object is equal to its mass times its acceleration, with both sides as vectors: F_net = m a. Here mass is a scalar that scales the acceleration vector, so the acceleration points in the same direction as the net force. The magnitude of acceleration is F_net divided by m.

This form is the general statement of the law. A specific case like F_net = m g would only apply when gravity is the only force acting, not in general. The idea that a = F_net / m^2 is incorrect because the mass should be in the denominator to first power, not squared. And work is not obtained by multiplying force by acceleration, so W = F_net a is not correct either. A valid rearrangement is a = F_net / m, which is equivalent to the vector form.