A body falls freely for 10 s. Its average velocity during this journey is (Take `g = 10 ms^(-2))`

Options

A. `100 ms^(-1)`
B. `10 ms^(-1)`
C. `50 ms^(-1)`
D. `5 ms^(-1)`

Answer

To find the average velocity of a body that falls freely for 10 seconds, we can follow these steps:

### Step 1: Understand the concept of free fall
A body in free fall is subject to gravitational acceleration (g). In this case, we are given that \( g = 10 \, \text{m/s}^2 \). The initial velocity (u) of the body is 0 since it starts from rest.

### Step 2: Use the formula for displacement in free fall
The displacement (h) of a freely falling body can be calculated using the formula:
\[ h = ut + \frac{1}{2} g t^2 \]
Since the initial velocity \( u = 0 \), the formula simplifies to:
\[ h = \frac{1}{2} g t^2 \]

### Step 3: Substitute the values into the formula
Now, substitute \( g = 10 \, \text{m/s}^2 \) and \( t = 10 \, \text{s} \) into the equation:
\[ h = \frac{1}{2} \times 10 \times (10)^2 \]
Calculating this gives:
\[ h = \frac{1}{2} \times 10 \times 100 = 5 \times 100 = 500 \, \text{m} \]

### Step 4: Calculate the average velocity
The average velocity (\( v_{\text{avg}} \)) is defined as the total displacement divided by the total time taken:
\[ v_{\text{avg}} = \frac{\Delta s}{\Delta t} \]
Here, \( \Delta s = h = 500 \, \text{m} \) and \( \Delta t = 10 \, \text{s} \):
\[ v_{\text{avg}} = \frac{500 \, \text{m}}{10 \, \text{s}} = 50 \, \text{m/s} \]

### Conclusion
The average velocity of the body during its free fall for 10 seconds is \( 50 \, \text{m/s} \).

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