Two bodies A and B start from rest from the same point with a uniform acceleration od `2 ms^(-2)` . If B starts one second later, then the two bodies are separated , at the end of the next second, by

Options

A. 1 m
B. 2 m
C. 3 m
D. 4 m

Explanation

To solve the problem, we need to calculate the distance traveled by both bodies A and B and then find the separation between them at the end of the second second after B starts moving.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Acceleration (a) = 2 m/s²
- Body A starts at t = 0 seconds.
- Body B starts at t = 1 second.

2. **Calculate the Distance Traveled by Body A in 2 Seconds:**
- Since A starts from rest, its initial velocity (u) = 0.
- The time (t) for A is 2 seconds when we want to find the distance at the end of the second second.
- Using the formula for distance:
\[ S_A = ut + \frac{1}{2} a t^2 \]
- Substituting the values:
\[ S_A = 0 \cdot 2 + \frac{1}{2} \cdot 2 \cdot (2)^2 \]
- Simplifying:
\[ S_A = 0 + 1 \cdot 4 = 4 \text{ meters} \]

3. **Calculate the Distance Traveled by Body B in 1 Second:**
- Body B starts moving at t = 1 second and travels for 1 second (from t = 1 to t = 2 seconds).
- Again, initial velocity (u) = 0.
- Time (t) for B is 1 second.
- Using the same formula for distance:
\[ S_B = ut + \frac{1}{2} a t^2 \]
- Substituting the values:
\[ S_B = 0 \cdot 1 + \frac{1}{2} \cdot 2 \cdot (1)^2 \]
- Simplifying:
\[ S_B = 0 + 1 \cdot 1 = 1 \text{ meter} \]

4. **Calculate the Separation Between A and B:**
- The separation (d) between A and B at the end of the second second is given by:
\[ d = S_A - S_B \]
- Substituting the distances:
\[ d = 4 \text{ meters} - 1 \text{ meter} = 3 \text{ meters} \]

5. **Final Answer:**
- The two bodies are separated by **3 meters** at the end of the second second.