A particle moves in east direction with 15m/sec for 2 sec then moves in northward with 5 m/s for 8 sec. A average speed of the particle is :-

Options

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

Answer

To find the average speed of the particle, we will follow these steps:

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

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

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

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

### Step 3: Calculate the total distance traveled
Now, we can find the total distance traveled by adding the distances from both directions.

\[ \text{Total Distance} = \text{Distance}_{\text{east}} + \text{Distance}_{\text{north}} = 30 \, \text{m} + 40 \, \text{m} = 70 \, \text{m} \]

### Step 4: Calculate the total time taken
The total time taken for the journey is the sum of the time spent in each direction.

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

### Step 5: Calculate the average speed
Finally, we can calculate the average speed using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{70 \, \text{m}}{10 \, \text{s}} = 7 \, \text{m/s} \]

Thus, the average speed of the particle is **7 m/s**.

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