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. (a)5N
B. (b)8.25N
C. (c)0.25N
D. (d)1N

Answer

To solve the problem step by step, we will use the principles of Newton's laws of motion.

### Given Data:
- Mass of the ball (m) = 0.5 kg
- Initial velocity (u) = 2 m/s
- Final velocity (v) = 3 m/s
- Time (t) = 2 s

### Step 1: Find the acceleration (a)
We can use the equation of motion:
\[ v = u + at \]

Rearranging the equation to solve for acceleration (a):
\[ a = \frac{v - u}{t} \]

Substituting the known values:
\[ a = \frac{3 \, \text{m/s} - 2 \, \text{m/s}}{2 \, \text{s}} \]
\[ a = \frac{1 \, \text{m/s}}{2 \, \text{s}} \]
\[ a = 0.5 \, \text{m/s}^2 \]

### Step 2: Calculate the force (F)
Using Newton's second law of motion:
\[ F = ma \]

Substituting the values of mass (m) and acceleration (a):
\[ F = 0.5 \, \text{kg} \times 0.5 \, \text{m/s}^2 \]
\[ F = 0.25 \, \text{N} \]

### Conclusion
The value of x (the force applied) is:
\[ x = 0.25 \, \text{N} \]