A particle moves in the direction of east for 2s with velocity of 15m/s .Then it moves towards north for 8s with a velocity of 5m/s . The average velocity of the particle is (in m/s)

Options

A. 1 m/s
B. 5 m/s
C. 7 m/s
D. 10 m/s

Answer

To find the average velocity of the particle, we can follow these steps:

### Step 1: Calculate the distance traveled in the east direction
The particle moves east for 2 seconds with a velocity of 15 m/s.

\[ \text{Distance}_{\text{east}} = \text{velocity} \times \text{time} = 15 \, \text{m/s} \times 2 \, \text{s} = 30 \, \text{m} \]

### Step 2: Calculate the distance traveled in the north direction
The particle then moves north for 8 seconds with a velocity of 5 m/s.

\[ \text{Distance}_{\text{north}} = \text{velocity} \times \text{time} = 5 \, \text{m/s} \times 8 \, \text{s} = 40 \, \text{m} \]

### Step 3: Determine the resultant displacement
The displacement can be found using the Pythagorean theorem since the movements are perpendicular to each other (east and north).

\[ \text{Displacement} = \sqrt{(\text{Distance}_{\text{east}})^2 + (\text{Distance}_{\text{north}})^2} \]

Substituting the values:

\[ \text{Displacement} = \sqrt{(30 \, \text{m})^2 + (40 \, \text{m})^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50 \, \text{m} \]

### Step 4: Calculate the total time of travel
The total time taken for the journey is the sum of the time taken in both directions.

\[ \text{Total time} = 2 \, \text{s} + 8 \, \text{s} = 10 \, \text{s} \]

### Step 5: Calculate the average velocity
Average velocity is defined as the total displacement divided by the total time taken.

\[ \text{Average velocity} = \frac{\text{Displacement}}{\text{Total time}} = \frac{50 \, \text{m}}{10 \, \text{s}} = 5 \, \text{m/s} \]

### Final Answer
The average velocity of the particle is \(5 \, \text{m/s}\).

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