A body of mass `2kg` starts from rest and moves with uniform acceleration. It acquires a velocity `20ms^-1` in `4s`.
Find average power transferred to the body in first `2s`.

Options

A. (a) `50W`
B. (b) `100W`
C. (c) `150W`
D. (d) `200W`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the acceleration of the body
Given:
- Mass of the body, \( m = 2 \, \text{kg} \)
- Initial velocity, \( u = 0 \, \text{m/s} \) (starts from rest)
- Final velocity, \( v = 20 \, \text{m/s} \)
- Time taken to reach this velocity, \( t = 4 \, \text{s} \)

Using the first equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ 20 = 0 + a \cdot 4 \]
Solving for \( a \):
\[ a = \frac{20}{4} = 5 \, \text{m/s}^2 \]

### Step 2: Calculate the displacement in the first 2 seconds
Using the second equation of motion:
\[ S = ut + \frac{1}{2} a t^2 \]
For the first 2 seconds, substituting \( u = 0 \), \( a = 5 \, \text{m/s}^2 \), and \( t = 2 \, \text{s} \):
\[ S = 0 \cdot 2 + \frac{1}{2} \cdot 5 \cdot (2)^2 \]
Calculating:
\[ S = 0 + \frac{1}{2} \cdot 5 \cdot 4 = 10 \, \text{m} \]

### Step 3: Calculate the work done on the body
Work done \( W \) is given by:
\[ W = F \cdot S \]
Where \( F = m \cdot a \):
\[ F = 2 \cdot 5 = 10 \, \text{N} \]
Now substituting \( F \) and \( S \):
\[ W = 10 \cdot 10 = 100 \, \text{J} \]

### Step 4: Calculate the average power transferred to the body in the first 2 seconds
Average power \( P \) is given by:
\[ P = \frac{W}{t} \]
Substituting \( W = 100 \, \text{J} \) and \( t = 2 \, \text{s} \):
\[ P = \frac{100}{2} = 50 \, \text{W} \]

### Final Answer
The average power transferred to the body in the first 2 seconds is \( 50 \, \text{W} \).

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