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Kinetic energy is the energy a body possesses due to its motion. It depends on the mass and velocity of the object. The formula for kinetic energy (KE) is given by \( KE = \frac{1}{2} mv^2 \), where \( m \) is the mass and \( v \) is the velocity.
In this exercise, the boy starts at rest relative to the moving walkway but increases in speed as he walks. His initial kinetic energy with respect to the walkway is zero, as he is initially standing still on it.
As he begins to walk, his speed increases to \( v \), giving him kinetic energy relative to the walkway. The work done by the force \( F \) results in this increase in his kinetic energy. The work-energy principle helps us understand how energy input, through force, translates into kinetic energy and motion.

Relative motion refers to the movement of an object with respect to another moving reference frame. In this situation, the boy's relative motion is his movement concerning the moving walkway. The speed \( v \) mentioned in the problem is his speed relative to this walkway and not to a fixed point on the ground.
Calculating relative motion is crucial when two objects are moving. In this case, the boy experiences a speed \( v \) relative to the walkway. His kinetic energy relative to the walkway is given by \(\frac{1}{2} m v^2 \). This type of calculation is often used in real-world scenarios where both objects are motionful, like in transportation where passengers move inside a moving vehicle.

Absolute motion considers an object's movement relative to a fixed, non-moving point. Here, the boy's absolute motion is his movement relative to the ground, not just the moving walkway. If the walkway moves with speed \( u \) and he moves relative to it with speed \( v \), then his absolute speed or velocity, \( x' \), is \( u + v \).
Understanding absolute motion is essential because it lets us compute the total actual movement. Whereas relative speed can change depending on the reference point, absolute speed remains constant when referred to a fixed base. It provides context for situations involving moving reference frames. In terms of energy, absolute kinetic energy involves the ground and is expressed as \( \frac{1}{2} m(u+v)^2 \).

Force and acceleration are closely related concepts in physics, described by Newton's second law. The boy applies a force \( F \) that results in his acceleration along the walkway. The relationship is given by:

• Force (\( F \)) = mass (\( m \)) \( \times \) acceleration (\( a \))

As the boy increases his velocity from rest to \( v \) relative to the walkway, he achieves acceleration. This force also contributes directly to the work done, which increases his kinetic energy. The average horizontal force exerted interacts with friction between the shoes and the walkway.
And why this matters? Because understanding force and acceleration aids in calculating changes in speed and direction, essential for analyzing motion. The work-energy equation combines force into how quickly a body's kinetic energy changes, offering a comprehensive view of dynamic systems.