Final answer:
The expression for kinetic energy is KE = 1/2mv², which indicates kinetic energy is proportional to the mass of the object and the square of its velocity. The incorrect formula KE = mv² lacks the division by 2, which is essential for the correct expression.
Step-by-step explanation:
The expression for the kinetic energy (KE) of an object with mass m moving at velocity v is derived from the work-energy principle. It states that the work done on an object is equal to the change in its kinetic energy. The correct formula for kinetic energy is KE = 1/2mv².
When an object with mass m is accelerated to a velocity v, the work done to accelerate the object is stored as kinetic energy. Since this energy is associated with the object's movement, any change in its speed results in a change in its kinetic energy. This concept leads us to the expression KE = 1/2mv², signifying that kinetic energy is proportional to the mass of an object and the square of its velocity.
If we were to consider the incorrect expression KE = (m)(v)² for kinetic energy, we would find that it lacks the correct factor of 1/2, making option c the correct critique of this formula.