Final Answer:
A small box of mass ( m ) is given a speed of ( v ).
Step-by-step explanation:
When a small box of mass ( m ) is given a speed ( v ), it acquires kinetic energy. The kinetic energy KE of an object can be calculated using the formula KE = 1/2 m v² ). In this case, the kinetic energy is directly proportional to the square of the speed of the box. This relationship implies that if the speed (v ) is increased, the kinetic energy will increase quadratically.
In physics, kinetic energy represents the ability of an object to do work due to its motion. When the box is given a speed, it gains kinetic energy, and the amount of energy depends on both the mass of the box (\( m \)) and the square of its speed ( v²). It's essential to consider the mass of the box because a heavier object would require more energy to achieve the same speed compared to a lighter object. Therefore, the speed (\( v \)) is a crucial factor in determining the kinetic energy and the subsequent behavior of the moving box.
In summary, the speed (v ) is a key parameter when considering the kinetic energy of a small box. The higher the speed, the greater the kinetic energy, and this energy is directly proportional to the square of the speed according to the kinetic energy formula. Understanding this relationship helps in analyzing the dynamics and energy aspects of a moving object, providing insights into its behavior and impact.