Following are three equations of motion
`S(g)=ut+(1)/(2)at^(2) v(s)=sqrt(u^(2)+2as) v(t)=u+at`
Where `,S,u,t,a,v` are respectively the displacement `(` dependent variable `)`, initial `(` constant `)`, time taken `(` independent variable `)`, acceleration `(` constant `)` and final velocity `(` dependent variable `)` of the particel after time `t`.
Find the displacement of the particle when its velocity becomes `10m//s` if acceleration is `5m//s^(2)` all through -

Options

A. `50 m`
B. `200 m`
C. `10 m`
D. `100 m`

Explanation

To find the displacement of the particle when its velocity becomes \(10 \, \text{m/s}\) and the acceleration is \(5 \, \text{m/s}^2\), we can use the equations of motion provided.

### Step-by-Step Solution:

1. **Identify the given values:**
- Final velocity, \(v = 10 \, \text{m/s}\)
- Acceleration, \(a = 5 \, \text{m/s}^2\)
- Initial velocity, \(u = 0 \, \text{m/s}\) (since the particle is at rest)

2. **Select the appropriate equation:**
We can use the second equation of motion:
\[ v^2 = u^2 + 2as \]
Here, \(s\) is the displacement we need to find.

3. **Substitute the known values into the equation:**
Since \(u = 0\), the equation simplifies to:
\[ v^2 = 0 + 2as \]
This can be rewritten as:
\[ v^2 = 2as \]

4. **Rearrange the equation to solve for \(s\):**
\[ s = \frac{v^2}{2a} \]

5. **Substitute the values of \(v\) and \(a\):**
\[ s = \frac{(10 \, \text{m/s})^2}{2 \times (5 \, \text{m/s}^2)} \]
\[ s = \frac{100 \, \text{m}^2/\text{s}^2}{10 \, \text{m/s}^2} \]

6. **Calculate the displacement:**
\[ s = 10 \, \text{m} \]

### Final Answer:
The displacement of the particle when its velocity becomes \(10 \, \text{m/s}\) is \(10 \, \text{m}\).

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