An insect crawls a distance distance of 4 m along North in 10 s and then a distance of 3 m along East in 5 s. The average velocity of the insect is

Options

A. `(7)/(15)ms^(-1)`
B. `(1)/(5)ms^(-1)`
C. `(1)/(3)ms^(-1)`
D. `(4)/(5)ms^(-1)`

Explanation

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

### Step 1: Understand the Motion
The insect moves in two segments:
1. It crawls 4 meters North in 10 seconds.
2. Then it crawls 3 meters East in 5 seconds.

### Step 2: Calculate Total Time Taken
The total time taken for the journey is the sum of the time taken for both segments:
- Time for the first segment = 10 seconds
- Time for the second segment = 5 seconds

Total time taken = 10 seconds + 5 seconds = 15 seconds.

### Step 3: Determine the Displacement
Displacement is the shortest distance between the initial and final positions of the insect. We can visualize this as a right triangle:
- The vertical leg (North) = 4 meters
- The horizontal leg (East) = 3 meters

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

### Step 4: Calculate Average Velocity
Average velocity is defined as the total displacement divided by the total time taken:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{5 \, \text{m}}{15 \, \text{s}} = \frac{1}{3} \, \text{m/s}. \]

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

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