If the average velocity of a body moving with uniform acceleration under the action of a force is ''v'' and the impulse it receives during a displacement of ''s'' is ''I'', the constant force acting on the body is given by 

Options

A. `(I xx v)/(2s)`
B. `(2I xx v)/(s) `
C. `(I xx v)/(s)`
D. `(I xx s)/(v)`

Answer

To solve the problem, we need to find the constant force acting on a body that is moving with uniform acceleration, given its average velocity \( v \), the impulse \( I \) received during a displacement \( s \).

### Step-by-Step Solution:

1. **Understanding Impulse**:
Impulse is defined as the product of force and the time duration over which the force acts. Mathematically, it can be expressed as:
\[ I = F \cdot T \]
where \( I \) is the impulse, \( F \) is the force, and \( T \) is the time duration.

2. **Relating Average Velocity and Time**:
The average velocity \( v \) is defined as the total displacement \( s \) divided by the total time \( T \):
\[ v = \frac{s}{T} \]
From this equation, we can express time \( T \) in terms of displacement \( s \) and average velocity \( v \):
\[ T = \frac{s}{v} \]

3. **Substituting Time into the Impulse Formula**:
Now, we can substitute \( T \) into the impulse formula:
\[ I = F \cdot \left(\frac{s}{v}\right) \]

4. **Rearranging to Find the Force**:
To find the force \( F \), we rearrange the equation:
\[ F = \frac{I \cdot v}{s} \]

5. **Final Expression for the Constant Force**:
Thus, the constant force acting on the body can be expressed as:
\[ F = \frac{v \cdot I}{s} \]

### Conclusion:
The constant force acting on the body is given by:
\[ F = \frac{v \cdot I}{s} \]