Here are three pairs of initial and final positions, respectively, along an `x` axis. Which pairs give a negative displacement : (a) -3 m, +5 m, (b) -3 m, - 7 m, (c) 7m, -3 m ?

Answer

To determine which pairs of initial and final positions give a negative displacement, we need to calculate the displacement for each pair using the formula:

**Displacement (Δx) = Final Position (x_f) - Initial Position (x_i)**

Let's analyze each pair step by step.

### Step 1: Analyze Pair (a) -3 m, +5 m
- **Initial Position (x_i)** = -3 m
- **Final Position (x_f)** = +5 m

**Calculation:**
\[ \Delta x = x_f - x_i = 5 - (-3) = 5 + 3 = 8 \text{ m} \]

**Displacement for Pair (a)**: +8 m (Positive)

### Step 2: Analyze Pair (b) -3 m, -7 m
- **Initial Position (x_i)** = -3 m
- **Final Position (x_f)** = -7 m

**Calculation:**
\[ \Delta x = x_f - x_i = -7 - (-3) = -7 + 3 = -4 \text{ m} \]

**Displacement for Pair (b)**: -4 m (Negative)

### Step 3: Analyze Pair (c) 7 m, -3 m
- **Initial Position (x_i)** = 7 m
- **Final Position (x_f)** = -3 m

**Calculation:**
\[ \Delta x = x_f - x_i = -3 - 7 = -10 \text{ m} \]

**Displacement for Pair (c)**: -10 m (Negative)

### Summary of Results:
- Pair (a): Displacement = +8 m (Positive)
- Pair (b): Displacement = -4 m (Negative)
- Pair (c): Displacement = -10 m (Negative)

### Final Answer:
The pairs that give a negative displacement are **(b) -3 m, -7 m** and **(c) 7 m, -3 m**.

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