The distance travelled by a freely falling body is proportional to

Options

A. the mass of the body
B. the square of the acceleration due to gravity
C. the square of the time of fall
D. the time of fall

Explanation

To solve the question regarding the distance traveled by a freely falling body, we can follow these steps:

### Step 1: Understand the Motion
A freely falling body is under the influence of gravity alone, which means it accelerates downwards at a constant rate, denoted by \( g \) (acceleration due to gravity).

### Step 2: Use the Equation of Motion
The equation of motion for an object under constant acceleration is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s \) is the distance traveled,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time of fall.

### Step 3: Set Initial Conditions
For a freely falling body dropped from rest:
- The initial velocity \( u = 0 \).
- The acceleration \( a = g \) (acceleration due to gravity).

### Step 4: Substitute Values
Substituting these values into the equation:
\[ s = 0 \cdot t + \frac{1}{2} g t^2 \]
This simplifies to:
\[ s = \frac{1}{2} g t^2 \]

### Step 5: Analyze the Result
From the equation \( s = \frac{1}{2} g t^2 \), we can see that the distance \( s \) is directly proportional to \( t^2 \) (the square of the time of fall).

### Conclusion
Thus, the distance traveled by a freely falling body is proportional to the square of the time of fall.

### Final Answer
The correct option is that the distance traveled by a freely falling body is proportional to the **square of the time of fall**.

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