A pump ejects 12000 kg of water at speed of 4m/s in 40 second. Find the average rate at which the pump is working.

Options

A. 0.24 KW
B. 2.4 W
C. 2.4 KW
D. 24 W

Answer

To find the average rate at which the pump is working, we can follow these steps:

### Step 1: Calculate the change in kinetic energy
The work done by the pump is equal to the change in kinetic energy of the water. The formula for kinetic energy (KE) is given by:

\[ KE = \frac{1}{2} mv^2 \]

where:
- \( m \) is the mass of the water (12000 kg),
- \( v \) is the final speed of the water (4 m/s).

Substituting the values:

\[ KE = \frac{1}{2} \times 12000 \, \text{kg} \times (4 \, \text{m/s})^2 \]

Calculating \( (4 \, \text{m/s})^2 \):

\[ (4 \, \text{m/s})^2 = 16 \, \text{m}^2/\text{s}^2 \]

Now substituting this back into the kinetic energy formula:

\[ KE = \frac{1}{2} \times 12000 \times 16 \]

Calculating:

\[ KE = 6000 \times 16 = 96000 \, \text{J} \]

### Step 2: Calculate the average power
Average power (\( P \)) is defined as the work done (or energy transferred) per unit time. The formula for average power is:

\[ P = \frac{\text{Work Done}}{\text{Time Taken}} \]

From the problem, we know:
- Work Done = 96000 J (from the kinetic energy calculation),
- Time Taken = 40 seconds.

Substituting these values into the power formula:

\[ P = \frac{96000 \, \text{J}}{40 \, \text{s}} \]

Calculating:

\[ P = 2400 \, \text{W} \]

### Step 3: Convert power to kilowatts
Since 1 kilowatt (kW) = 1000 watts (W), we can convert the power:

\[ P = \frac{2400 \, \text{W}}{1000} = 2.4 \, \text{kW} \]

### Final Answer
The average rate at which the pump is working is **2.4 kW**.

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