Understanding the Concepts

* Work: Work is done when a force causes an object to move a certain distance. It's calculated by: Work (W) = Force (F) x Distance (d)

* Constant Velocity: If an object is moving at a constant velocity, the net force acting on it is zero. This means the force the boy applies is equal and opposite to the force of friction.

* Kinetic Energy: The energy of motion is called kinetic energy. It's calculated by: Kinetic Energy (KE) = (1/2) * Mass (m) * Velocity (v)²

Solving the Problem

1. Calculate the initial kinetic energy:

* KE₁ = (1/2) * 30 kg * (0.5 m/s)² = 3.75 J

2. Calculate the final kinetic energy:

* KE₂ = (1/2) * 30 kg * (1.0 m/s)² = 15 J

3. Find the change in kinetic energy:

* ΔKE = KE₂ - KE₁ = 15 J - 3.75 J = 11.25 J

Important Note: Since the boy is pushing the box at a constant velocity initially, the work he does is only overcoming friction. When he increases the velocity, he does additional work to increase the box's kinetic energy.

Therefore, the boy does 11.25 Joules of work on the box to increase its velocity from 0.5 m/s to 1.0 m/s.