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 :-

Explanation

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.

\[ \text{Distance}_{\text{east}} = \text{Speed} \times \text{Time} = 15 \, \text{m/s} \times 2 \, \text{s} = 30 \, \text{meters} \]

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

\[ \text{Distance}_{\text{north}} = \text{Speed} \times \text{Time} = 5 \, \text{m/s} \times 8 \, \text{s} = 40 \, \text{meters} \]

### Step 3: Calculate the total distance traveled.
Now, we add the distances traveled in both directions to find the total distance.

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

### Step 4: Calculate the total time taken.
Next, we calculate the total time taken for the entire journey.

\[ \text{Total Time} = \text{Time}_{\text{east}} + \text{Time}_{\text{north}} = 2 \, \text{s} + 8 \, \text{s} = 10 \, \text{seconds} \]

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

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

### Final Answer:
The average speed of the particle is **7 m/s**.

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