A block of mass 10 kg accelerates uniformly from rest to a speed of 2 m/s in 20 sec. The average power developed in time interval of 0 to 20 sec is

Options

A. 10W
B. 1W
C. 20W
D. 2W

Answer

To solve the problem, we need to calculate the average power developed by the block during the time interval from 0 to 20 seconds. We can do this by following these steps:

### Step 1: Identify the given values
- Mass of the block (m) = 10 kg
- Initial velocity (u) = 0 m/s (the block starts from rest)
- Final velocity (v) = 2 m/s
- Time (t) = 20 s

### Step 2: Calculate the change in kinetic energy
The work done on the block can be calculated using the change in kinetic energy formula:

\[ \text{Work} = \Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m u^2 \]

Substituting the known values:

\[ \Delta KE = \frac{1}{2} \times 10 \, \text{kg} \times (2 \, \text{m/s})^2 - \frac{1}{2} \times 10 \, \text{kg} \times (0 \, \text{m/s})^2 \]

Calculating this gives:

\[ \Delta KE = \frac{1}{2} \times 10 \times 4 - 0 = 20 \, \text{J} \]

### Step 3: Calculate the average power
Power is defined as the rate of doing work, which can be calculated using the formula:

\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \]

Substituting the values we found:

\[ \text{Power} = \frac{20 \, \text{J}}{20 \, \text{s}} = 1 \, \text{W} \]

### Conclusion
The average power developed in the time interval from 0 to 20 seconds is **1 watt**.

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