An insect craws a distance of 3m along north in 6 seconds and then a distance of 4 m along east in 9 seconds. Then the average velocity of the insect is

Options

A. `3 ms^(-1)`
B. `10 ms^(-1)`
C. `(17)/(18) ms^(-1)`
D. `1/3 ms^(-1)`

Explanation

To find the average velocity of the insect, we need to follow these steps:

### Step 1: Understand the Motion
The insect crawls:
- 3 meters north in 6 seconds.
- Then, it crawls 4 meters east in 9 seconds.

### Step 2: Calculate Total Displacement
Displacement is the shortest distance from the initial position to the final position. We can visualize the insect's path as a right triangle:
- The northward movement (3 m) and the eastward movement (4 m) form the two legs of the triangle.

Using the Pythagorean theorem:
\[ \text{Displacement} = \sqrt{(3 \, \text{m})^2 + (4 \, \text{m})^2} \]
\[ = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{m} \]

### Step 3: Calculate Total Time
Total time taken for the journey is the sum of the time taken for each segment:
\[ \text{Total Time} = 6 \, \text{seconds} + 9 \, \text{seconds} = 15 \, \text{seconds} \]

### Step 4: Calculate Average Velocity
Average velocity is given by the formula:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
Substituting the values we found:
\[ \text{Average Velocity} = \frac{5 \, \text{m}}{15 \, \text{s}} = \frac{1}{3} \, \text{m/s} \]

### Final Answer
The average velocity of the insect is \(\frac{1}{3} \, \text{m/s}\).

---