A body moves along the sides AB, BC and CD of a square of side 10 meter with velocity of constant magnitude 3 meter/sec. Its average velocity will be-

Options

A. 3 m/sec
B. 0.87 m/sec
C. 1.33 m/sec
D. 1 m/sec

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the motion of the body
The body moves along the sides AB, BC, and CD of a square with each side measuring 10 meters. The body starts at point A and ends at point D after moving through points B and C.

### Step 2: Identify the initial and final points
- Initial point (A)
- Final point (D)

### Step 3: Calculate the total displacement
Displacement is defined as the shortest distance between the initial and final points. In this case, the body moves from point A to point D, which is a straight line across one side of the square.

- Since the side of the square is 10 meters, the displacement from A to D is:
\[ \text{Displacement} = 10 \text{ meters} \]

### Step 4: Calculate the total distance traveled
The body travels along three sides of the square:
- Distance from A to B = 10 meters
- Distance from B to C = 10 meters
- Distance from C to D = 10 meters

Total distance traveled is:
\[ \text{Total Distance} = 10 + 10 + 10 = 30 \text{ meters} \]

### Step 5: Calculate the total time taken
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \Rightarrow \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:
\[ \text{Total Time} = \frac{30 \text{ meters}}{3 \text{ meters/second}} = 10 \text{ seconds} \]

### Step 6: Calculate the average velocity
The formula for average velocity is:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \]

Substituting the values:
\[ \text{Average Velocity} = \frac{10 \text{ meters}}{10 \text{ seconds}} = 1 \text{ meter/second} \]

### Conclusion
The average velocity of the body is:
\[ \text{Average Velocity} = 1 \text{ meter/second} \]