A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. Its initial velocity will be

Options

A. 4 m/s
B. 2.5 m/s
C. 5.5 m/s
D. 11 m/s

Explanation

To solve the problem step by step, we will use the equations of motion for uniformly accelerated motion.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Distance covered in the first 5 seconds (S1) = 40 m
- Distance covered in the next 5 seconds (S2) = 65 m
- Time for both distances (T) = 5 s

2. **Use the Equation of Motion:**
The equation for distance covered under uniform acceleration is:
\[ S = Ut + \frac{1}{2}At^2 \]
where:
- \( S \) = distance
- \( U \) = initial velocity
- \( A \) = acceleration
- \( t \) = time

3. **Apply the Equation for the First 5 Seconds (S1):**
For the first 5 seconds:
\[ S_1 = U \cdot T + \frac{1}{2} A T^2 \]
Substituting the values:
\[ 40 = U \cdot 5 + \frac{1}{2} A (5^2) \]
Simplifying this gives:
\[ 40 = 5U + \frac{25}{2} A \quad \text{(Equation 1)} \]

4. **Apply the Equation for the Next 5 Seconds (S2):**
For the next 5 seconds, the total time is now 10 seconds. The distance covered in the second interval (from 5s to 10s) is:
\[ S_2 = V \cdot T + \frac{1}{2} A T^2 \]
where \( V \) is the final velocity after the first 5 seconds. We know:
\[ V = U + A \cdot T \]
Substituting \( V \) into the equation for S2:
\[ 65 = (U + A \cdot 5) \cdot 5 + \frac{1}{2} A (5^2) \]
Simplifying this gives:
\[ 65 = 5U + 25A + \frac{25}{2} A \]
Combining terms:
\[ 65 = 5U + 25A + 12.5A \]
\[ 65 = 5U + 37.5A \quad \text{(Equation 2)} \]

5. **Subtract Equation 1 from Equation 2:**
Now we will subtract Equation 1 from Equation 2 to eliminate \( U \):
\[ (65 - 40) = (5U + 37.5A) - (5U + 12.5A) \]
This simplifies to:
\[ 25 = 25A \]
Therefore, we find:
\[ A = 1 \, \text{m/s}^2 \]

6. **Substitute A back into Equation 1 to find U:**
Now substitute \( A \) back into Equation 1:
\[ 40 = 5U + \frac{25}{2} \cdot 1 \]
Simplifying gives:
\[ 40 = 5U + 12.5 \]
\[ 5U = 40 - 12.5 \]
\[ 5U = 27.5 \]
\[ U = \frac{27.5}{5} = 5.5 \, \text{m/s} \]

### Final Answer:
The initial velocity \( U \) is **5.5 m/s**.