An object of mass 30 kg is in free fall in a vacuum where there is no air resistance. Determine the acceleration of the object.

1. Break Down the Problem

To determine the acceleration of an object in free fall, we need to consider the fact that in a vacuum, the only force acting on the object is gravity. We will use the following information:

• Mass of the object: $m = 30 \, \text{kg}$
• Acceleration due to gravity: $g \approx 9.81 \, \text{m/s}^2$

2. Relevant Concepts

The acceleration of an object in free fall, when only gravitational force is acting on it, is equal to the acceleration due to gravity. This can be represented mathematically as: $a = g$ where:

• $a$ is the acceleration of the object,
• $g$ is the acceleration due to gravity ($9.81 \, \text{m/s}^2$).

3. Analysis and Detail

Since the object is in a vacuum, we ignore other forces like air resistance. Thus, we directly conclude that: $a = 9.81 \, \text{m/s}^2$

4. Verify and Summarize

We calculated that the acceleration of an object in free fall is $9.81 \, \text{m/s}^2$. This value is standard and widely accepted for the acceleration due to gravity near the surface of the Earth.

Final Answer

The acceleration of the object is $9.81 \, \text{m/s}^2$.