Yes, the work done on an object can depend on its velocity. Work is defined as the transfer of energy that occurs when a force is applied to an object and it moves through a displacement. Mathematically, work (W) is calculated as the dot product of the force (F) applied to the object and the displacement (d) of the object:
W = F * d * cos(theta)
where theta is the angle between the force vector and the displacement vector.
In this equation, the magnitude of the force, the magnitude of the displacement, and the angle between the force and displacement vectors all play a role in determining the work done. The velocity of the object is related to its displacement over time. If the velocity changes, it affects the rate at which the object covers the displacement, which can impact the amount of work done.
For example, if a constant force is applied to an object, and the object moves a greater distance in the same amount of time (increasing its velocity), then more work will be done compared to when the object moves a shorter distance in the same amount of time (decreasing its velocity). This is because the displacement component in the work equation becomes larger when the velocity is higher, resulting in more work done.
In summary, the velocity of the body can indeed influence the amount of work done on it, along with other factors such as the magnitude of the force and the angle between the force and displacement vectors.