A particle moves in the direction of east for 2s with velocity of `15 ms^(-1).` Then it moves towards north for 8s with a a velocity of `5 ms^(-1).` The average velocity of the particle is

Options

A. `1ms ^(-1)`
B. `5ms ^(-1)`
C. `7ms^(-1)`
D. `10ms^(-1)`

Answer

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

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

Displacement (East) = Velocity × Time
Displacement (East) = 15 m/s × 2 s = 30 m

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

Displacement (North) = Velocity × Time
Displacement (North) = 5 m/s × 8 s = 40 m

### Step 3: Determine the total displacement
The total displacement can be found using the Pythagorean theorem since the displacements in the east and north directions are perpendicular to each other.

Total Displacement = √(Displacement (East)² + Displacement (North)²)
Total Displacement = √(30 m)² + (40 m)²
Total Displacement = √(900 + 1600)
Total Displacement = √2500
Total Displacement = 50 m

### Step 4: Calculate the total time of travel
Total time = Time (East) + Time (North)
Total time = 2 s + 8 s = 10 s

### Step 5: Calculate the average velocity
Average Velocity = Total Displacement / Total Time
Average Velocity = 50 m / 10 s = 5 m/s

### Final Answer
The average velocity of the particle is **5 m/s**.

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