In 20 seconds, the speed of a motor changes from 1200 rpm to 1800 .In this period , of number of revoutions completed by it is

Options

A. 500
B. 400
C. 200
D. 100

Explanation

To solve the problem of how many revolutions a motor completes while its speed changes from 1200 RPM to 1800 RPM over a period of 20 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Convert RPM to RPS**:
- The initial speed \( N_1 \) is given as 1200 RPM. To convert this to revolutions per second (RPS), we use the conversion factor \( \frac{1 \text{ minute}}{60 \text{ seconds}} \):
\[ N_1 = \frac{1200 \text{ revolutions}}{1 \text{ minute}} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = \frac{1200}{60} = 20 \text{ RPS} \]

2. **Convert the final speed to RPS**:
- The final speed \( N_2 \) is given as 1800 RPM. Using the same conversion:
\[ N_2 = \frac{1800 \text{ revolutions}}{1 \text{ minute}} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = \frac{1800}{60} = 30 \text{ RPS} \]

3. **Calculate the average speed**:
- The average speed \( N \) during the time interval can be calculated as:
\[ N = \frac{N_1 + N_2}{2} = \frac{20 + 30}{2} = \frac{50}{2} = 25 \text{ RPS} \]

4. **Calculate the total number of revolutions**:
- The total number of revolutions \( R \) completed in 20 seconds can be calculated using the formula:
\[ R = N \times T \]
where \( T \) is the time in seconds. Substituting the values:
\[ R = 25 \text{ RPS} \times 20 \text{ seconds} = 500 \text{ revolutions} \]

### Final Answer:
The number of revolutions completed by the motor in 20 seconds is **500 revolutions**.

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