A ball of mass 0.5 kg is moving with a velocity of 2`ms^(-1)`. It if subjected to a force of x Newton for 2s. Because of this force, the ball moves with a velocity of `3ms^(-1)` . The value of x is `:`

Options

A. 5N
B. 8.25N
C. 0.25N
D. 1N

Answer

To solve the problem, we will use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a). We will also use the formula for acceleration, which is defined as the change in velocity over time.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the ball (m) = 0.5 kg
- Initial velocity (u) = 2 m/s
- Final velocity (v) = 3 m/s
- Time (t) = 2 s

2. **Calculate the acceleration (a):**
- The formula for acceleration is given by:
\[ a = \frac{v - u}{t} \]
- Substituting the values:
\[ a = \frac{3 \, \text{m/s} - 2 \, \text{m/s}}{2 \, \text{s}} = \frac{1 \, \text{m/s}}{2 \, \text{s}} = 0.5 \, \text{m/s}^2 \]

3. **Apply Newton's second law to find the force (x):**
- According to Newton's second law:
\[ F = m \cdot a \]
- Substituting the values of mass and acceleration:
\[ F = 0.5 \, \text{kg} \cdot 0.5 \, \text{m/s}^2 = 0.25 \, \text{N} \]

4. **Conclusion:**
- The value of the force \( x \) is \( 0.25 \, \text{N} \).

### Final Answer:
The value of \( x \) is \( 0.25 \, \text{N} \).

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