Question

1. a student conducts an experiment where they apply different forces to objects of varying masses and measure the resulting acceleration. the data is recorded in the table.

mass (kg)	force (n)	acceleration (m/s²)
4	10	2.5
6	10	1.67
8	10	1.25

based on the data, which statement best describes the relationship between mass and acceleration when the force is kept constant?

• the acceleration of the object increases as the mass increases, indicating a direct relationship between mass and acceleration.
• the acceleration of the object decreases as the mass increases, demonstrating an inverse relationship between mass and acceleration.
• the acceleration remains constant regardless of the mass, showing that mass has no effect on acceleration when force is constant.
• the acceleration initially increases with mass, but then decreases as mass continues to increase, indicating an inverse relationship.

Explanation:

To determine the relationship between mass and acceleration when force is constant, we analyze the data:

• When mass increases from 2 kg to 4 kg to 6 kg to 8 kg (while force remains 10 N), acceleration decreases from 5 m/s² to 2.5 m/s² to 1.67 m/s² to 1.25 m/s².
• A direct relationship would mean both variables increase together, but here acceleration decreases as mass increases.
• A constant acceleration would mean no change, which is not the case.
• The acceleration does not first increase then decrease; it consistently decreases with increasing mass, demonstrating an inverse relationship (as one increases, the other decreases when force is constant, consistent with Newton's second law \( F = ma \) or \( a=\frac{F}{m} \), so \( a \propto \frac{1}{m} \) when \( F \) is constant).

Answer:

The option: "The acceleration of the object decreases as the mass increases, demonstrating an inverse relationship between mass and acceleration."