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 a particle after 10 seconds starting from rest with a uniform acceleration of `2m//s^(2)`

Options

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

Explanation

To find the displacement of a particle after 10 seconds starting from rest with a uniform acceleration of \(2 \, \text{m/s}^2\), we will use the first equation of motion:

\[ S = ut + \frac{1}{2} a t^2 \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial velocity (\(u\)) = 0 (since the particle starts from rest)
- Time taken (\(t\)) = 10 seconds
- Acceleration (\(a\)) = \(2 \, \text{m/s}^2\)

2. **Substitute the values into the equation:**
\[ S = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ S = (0)(10) + \frac{1}{2} (2) (10^2) \]

3. **Calculate the first term:**
\[ (0)(10) = 0 \]

4. **Calculate the second term:**
\[ \frac{1}{2} (2) (10^2) = \frac{1}{2} (2) (100) = 1 \times 100 = 100 \]

5. **Combine the results:**
\[ S = 0 + 100 = 100 \, \text{meters} \]

### Final Result:
The displacement of the particle after 10 seconds is \(100 \, \text{meters}\).

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