## To determine which work is required to stop a moving object, we need to understand the concept of work and the factors involved. Work is defined as the transfer of energy resulting from the application of a force. In this case, the work required to stop a moving object refers to the work done to counteract the object's motion and bring it to a state of rest.

To calculate the work required to stop the object, we need to consider the change in kinetic energy (KE) of the object. Kinetic energy is the energy possessed by an object due to its motion and is given by the equation KE = (1/2) * m * v^2, where m represents the mass of the object and v represents its velocity or speed.

Now, let's analyze the given options:

- Initial speed: The initial speed of the object alone does not directly determine the amount of work required to stop it. The work done is related to the change in kinetic energy, not the initial speed alone.

- Initial kinetic energy of the object: This option aligns with the concept mentioned earlier. When an object is brought to rest, its final kinetic energy becomes zero. Therefore, the work done is equal to the initial kinetic energy. So, this answer is correct.

- Mass of the object times its acceleration: This option is related to force, given by the equation F = m * a, where F represents force, m is the mass of the object, and a is the acceleration. While force is essential in bringing an object to rest, it does not directly relate to the work done to stop it.

- Mass of the object times its initial speed: Similar to the previous option, this equation represents momentum (p = m * v) rather than work. It does not provide information about the work required to stop the object.

- Square of the initial speed of the object: The square of the initial speed is related to kinetic energy but does not represent the work done to stop the object directly. It can be used to calculate the initial kinetic energy, but it does not answer the question of the work required to stop the object.

Therefore, the correct answer to the question is the initial kinetic energy of the object, as this directly relates to the work required to bring it to rest.