Final answer:
Kinetic energy acquired by a body is directly proportional to the square of the distance traveled when starting from rest under a constant force.
Step-by-step explanation:
The kinetic energy acquired by a body of mass m traveling some distance s, starting from rest under the action of a constant force, is directly proportional to the square of the distance traveled (s²). This relationship can be understood through the work-energy principle which states that the work done on an object is equal to its change in kinetic energy.
Given that work is the product of force and displacement (W = F × s), and assuming the force is constant, as the object moves under this constant force, its kinetic energy would be directly related to the work done on it.
When the object is initially at rest, all of the work done on it translates into kinetic energy (KE), hence KE is also proportional to the force times the distance squared when the force is constant.
The precise relationship is derived from integrating the force over the distance traveled, but this level of derivation may extend beyond basic high school physics.