To solve this problem, we can use Newton's Second Law of Motion, which states:

$F = ma$

Where:

• $F$ is the force applied,
• $m$ is the mass of the object,
• $a$ is the acceleration of the object.

Given:

• Box 2 has twice the mass of Box 1 ($m_2 = 2m_1$).
• The same force $F$ is applied to both boxes for the same time duration.

Step 1: Determine Acceleration

From Newton's second law:

$a_1 = \frac{F}{m_1}, \quad a_2 = \frac{F}{m_2} = \frac{F}{2m_1} = \frac{a_1}{2}$

This shows that the acceleration of Box 2 is half of that of Box 1.

Step 2: Relate Acceleration to Velocity Change

The change in velocity ($\Delta v$) for a given acceleration over time $t$ is:

$\Delta v = a \cdot t$

Since both boxes experience the same force for the same time $t$:

$\Delta v_1 = a_1 \cdot t, \quad \Delta v_2 = a_2 \cdot t = \frac{a_1}{2} \cdot t = \frac{\Delta v_1}{2}$

Conclusion

The lighter box (Box 1) has a greater change in velocity than the heavier box (Box 2).

So, the correct answer is:

• The lighter box has a greater change in velocity.

Would you like further details on this explanation? Here are five related questions to expand on this topic:

1. How does mass affect the acceleration of an object when the same force is applied?
2. What would happen if the force applied was different for the two boxes?
3. Can you explain the relationship between force, mass, and acceleration with an example?
4. How does the concept of momentum relate to the problem of the two boxes?
5. If the force was applied for a shorter duration, how would that affect the change in velocity?

Tip: Remember, acceleration is inversely proportional to mass when the force is constant. This principle is crucial in understanding how objects of different masses respond to the same force.