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 step by step, we will calculate the average power developed by the block during the time interval of 0 to 20 seconds.

### Step 1: Determine the acceleration of the block.
Given:
- Initial velocity (u) = 0 m/s (since the block starts from rest)
- Final velocity (v) = 2 m/s
- Time (t) = 20 s

Using the formula for acceleration (a):
\[ a = \frac{v - u}{t} = \frac{2 \, \text{m/s} - 0 \, \text{m/s}}{20 \, \text{s}} = \frac{2}{20} = 0.1 \, \text{m/s}^2 \]

### Step 2: Calculate the force acting on the block.
Using Newton's second law:
\[ F = m \cdot a \]
Where:
- Mass (m) = 10 kg
- Acceleration (a) = 0.1 m/s²

Calculating the force:
\[ F = 10 \, \text{kg} \cdot 0.1 \, \text{m/s}^2 = 1 \, \text{N} \]

### Step 3: Calculate the displacement of the block.
Using the formula for displacement (s) under uniform acceleration:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- Initial velocity (u) = 0 m/s
- Acceleration (a) = 0.1 m/s²
- Time (t) = 20 s

Calculating the displacement:
\[ s = 0 \cdot 20 + \frac{1}{2} \cdot 0.1 \cdot (20)^2 = 0 + \frac{1}{2} \cdot 0.1 \cdot 400 = 0.05 \cdot 400 = 20 \, \text{m} \]

### Step 4: Calculate the work done by the block.
Work done (W) is given by:
\[ W = F \cdot s \]
Where:
- Force (F) = 1 N
- Displacement (s) = 20 m

Calculating the work done:
\[ W = 1 \, \text{N} \cdot 20 \, \text{m} = 20 \, \text{J} \]

### Step 5: Calculate the average power developed.
Average power (P) is given by:
\[ P = \frac{W}{t} \]
Where:
- Work done (W) = 20 J
- Time (t) = 20 s

Calculating the average power:
\[ P = \frac{20 \, \text{J}}{20 \, \text{s}} = 1 \, \text{W} \]

### Final Answer:
The average power developed in the time interval of 0 to 20 seconds is **1 Watt**.

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