A particle starts from rest with uniform acceleration and covers 26m in 7th second find its displacement in 9th sec

Options

A. 38 m
B. 34 m
C. 32 m
D. 30 m

Answer

To solve the problem step by step, we will use the equations of motion and the concept of displacement in a specific time interval.

### Step 1: Understand the Problem
We need to find the displacement of a particle in the 9th second, given that it starts from rest with uniform acceleration and covers 26 meters in the 7th second.

### Step 2: Use the Formula for Displacement in the nth Second
The displacement \( s_n \) in the nth second can be calculated using the formula:
\[ s_n = u + \frac{a}{2}(2n - 1) \]
where:
- \( u \) is the initial velocity,
- \( a \) is the uniform acceleration,
- \( n \) is the second for which we want to find the displacement.

### Step 3: Find the Acceleration
We know that the particle covers 26 meters in the 7th second. We can set \( n = 7 \) in the formula:
\[ s_7 = u + \frac{a}{2}(2 \times 7 - 1) = 26 \]
Since the particle starts from rest, \( u = 0 \):
\[ 0 + \frac{a}{2}(14 - 1) = 26 \]
\[ \frac{a}{2} \times 13 = 26 \]
\[ \frac{a}{2} = 2 \quad \Rightarrow \quad a = 4 \, \text{m/s}^2 \]

### Step 4: Calculate the Displacement in the 9th Second
Now, we need to find the displacement in the 9th second using the same formula:
\[ s_9 = u + \frac{a}{2}(2 \times 9 - 1) \]
Substituting \( u = 0 \) and \( a = 4 \):
\[ s_9 = 0 + \frac{4}{2}(18 - 1) \]
\[ s_9 = 2 \times 17 = 34 \, \text{m} \]

### Final Answer
The displacement of the particle in the 9th second is **34 meters**.

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