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 while its speed increases uniformly from 600 rpm to 1200 rpm in 10 seconds, we can follow these steps:

### Step 1: Convert RPM to RPS
First, we need to convert the initial and final speeds from revolutions per minute (rpm) to revolutions per second (rps).

- Initial speed (ω_initial) = 600 rpm = \( \frac{600}{60} \) rps = 10 rps
- Final speed (ω_final) = 1200 rpm = \( \frac{1200}{60} \) rps = 20 rps

### Step 2: Calculate Angular Acceleration
Next, we need to find the angular acceleration (α) using the formula:
\[ \omega_{final} = \omega_{initial} + \alpha t \]
Rearranging gives us:
\[ \alpha = \frac{\omega_{final} - \omega_{initial}}{t} \]
Substituting the values:
\[ \alpha = \frac{20 \, \text{rps} - 10 \, \text{rps}}{10 \, \text{s}} = \frac{10 \, \text{rps}}{10 \, \text{s}} = 1 \, \text{rps}^2 \]

### Step 3: Calculate Total Revolutions
Now, we can calculate the total angle (θ) in revolutions using the formula:
\[ \theta = \omega_{initial} t + \frac{1}{2} \alpha t^2 \]
Substituting the known values:
\[ \theta = (10 \, \text{rps})(10 \, \text{s}) + \frac{1}{2}(1 \, \text{rps}^2)(10 \, \text{s})^2 \]
Calculating each term:
\[ \theta = 100 \, \text{revolutions} + \frac{1}{2}(1)(100) = 100 + 50 = 150 \, \text{revolutions} \]

### Conclusion
The motor makes a total of **150 revolutions** during the 10 seconds.

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