A particle starts moving with acceleration `2 m//s^(2)`. Distance travelled by it in `5^(th)` half second is

Options

A. 1.25 m
B. 2.25 m
C. 6.25 m
D. 30.25 m

Answer

To solve the problem of finding the distance travelled by a particle with an acceleration of \(2 \, \text{m/s}^2\) in the fifth half second, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Time Intervals**:
- The fifth half second refers to the time interval from \(2\) seconds to \(2.5\) seconds. This means we need to calculate the distance travelled from \(t = 2 \, \text{s}\) to \(t = 2.5 \, \text{s}\).

2. **Use the Distance Formula**:
- The formula for distance travelled under constant acceleration is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
- Here, \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time.

3. **Calculate Distance at \(t = 2.5 \, \text{s}\)**:
- Given \(u = 0\) (the particle starts from rest) and \(a = 2 \, \text{m/s}^2\):
\[ s_1 = 0 + \frac{1}{2} \times 2 \times (2.5)^2 \]
- Calculate \(s_1\):
\[ s_1 = 1 \times 6.25 = 6.25 \, \text{m} \]

4. **Calculate Distance at \(t = 2 \, \text{s}\)**:
- Now, calculate the distance travelled by the particle at \(t = 2 \, \text{s}\):
\[ s_2 = 0 + \frac{1}{2} \times 2 \times (2)^2 \]
- Calculate \(s_2\):
\[ s_2 = 1 \times 4 = 4 \, \text{m} \]

5. **Find the Distance in the Fifth Half Second**:
- The distance travelled in the fifth half second is given by:
\[ \text{Distance in 5th half second} = s_1 - s_2 \]
- Substitute the values:
\[ \text{Distance} = 6.25 - 4 = 2.25 \, \text{m} \]

### Final Answer:
The distance travelled by the particle in the fifth half second is \(2.25 \, \text{m}\).

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