Distance is a scalar quantity. Displacement is a vector quqntity. The magnitude of displacement is always less than or equal to distance. For a moving body displacement can be zero but distance cannot be zero. Same concept is applicable regarding velocity and speed. Acceleration is the rate of change of velocity. If acceleration is constant, then equations of kinematics are applicable for one dimensional motion under the gravity in which air resistance is considered, then the value of acceleration depends on the density of medium. Each motion is measured with respect of frame of reference. Relative velocity may be greater`//` smaller to the individual velocities.
A person is going 40 m north, 30m east and then `30sqrt(2) m` southwest. The net displacement will be

Options

A. 10 m towards east
B. 10 m towards west
C. 10 m towards south
D. 10 m towards north

Explanation

To find the net displacement of the person who moves 40 m north, 30 m east, and then 30√2 m southwest, we can follow these steps:

### Step 1: Represent the Movements
1. **North Movement**: The person moves 40 m north. This can be represented as a vector in the positive y-direction.
2. **East Movement**: The person then moves 30 m east. This can be represented as a vector in the positive x-direction.
3. **Southwest Movement**: Finally, the person moves 30√2 m southwest. The southwest direction is at a 45-degree angle between south and west.

### Step 2: Break Down the Southwest Movement
The southwest movement can be broken down into its x and y components:
- The x-component (west) is:
\[ \text{SW}_x = -\frac{30\sqrt{2}}{\sqrt{2}} = -30 \text{ m} \]
- The y-component (south) is:
\[ \text{SW}_y = -\frac{30\sqrt{2}}{\sqrt{2}} = -30 \text{ m} \]

### Step 3: Calculate the Total Displacement in Each Direction
Now, we can calculate the total displacement in the x and y directions:
- **Total displacement in the x-direction**:
\[ \text{Total}_x = 30 \text{ m (east)} - 30 \text{ m (west)} = 0 \text{ m} \]
- **Total displacement in the y-direction**:
\[ \text{Total}_y = 40 \text{ m (north)} - 30 \text{ m (south)} = 10 \text{ m} \]

### Step 4: Determine the Net Displacement
The net displacement can be represented as a vector from the origin to the final position:
- Since the total x-displacement is 0 m and the total y-displacement is 10 m, the net displacement is:
\[ \text{Net Displacement} = 10 \text{ m (north)} \]

### Final Answer
The net displacement of the person is **10 meters towards north**.

---