The speed of a motor increases uniformly from 600 rpm to 1200 rpm in 10 second. How many revolutions does it make in this period

Options

A. 150
B. 250
C. 300
D. 325

Explanation

To solve the problem of how many revolutions a motor makes as its speed increases uniformly from 600 rpm to 1200 rpm in 10 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Convert RPM to RPS**:
- The initial speed (ω_initial) is 600 revolutions per minute (rpm).
- The final speed (ω_final) is 1200 revolutions per minute (rpm).
- To work in seconds, we convert these values to revolutions per second (rps):
- ω_initial = 600 rpm ÷ 60 = 10 rps
- ω_final = 1200 rpm ÷ 60 = 20 rps

2. **Calculate the Average Speed**:
- The average speed (ω_avg) during the time interval can be calculated as:
\[ \omega_{avg} = \frac{\omega_{initial} + \omega_{final}}{2} \]
- Substituting the values:
\[ \omega_{avg} = \frac{10 + 20}{2} = \frac{30}{2} = 15 \text{ rps} \]

3. **Calculate the Total Time**:
- The total time (t) during which the speed increases is given as 10 seconds.

4. **Calculate the Total Revolutions**:
- The total number of revolutions (N) made during this time can be calculated using the formula:
\[ N = \omega_{avg} \times t \]
- Substituting the values:
\[ N = 15 \text{ rps} \times 10 \text{ s} = 150 \text{ revolutions} \]

### Final Answer:
The motor makes **150 revolutions** during the 10 seconds of acceleration from 600 rpm to 1200 rpm.

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