A body of mass 50 kg is at rest. The work doen to accelerate it by 20m/s in 10 s is

Options

A. `10^(3)J`
B. `10^(4)J`
C. `2xx10^(3)J`
D. `4xx10^(4)J`

Explanation

To solve the problem step by step, we will calculate the work done to accelerate a body of mass 50 kg from rest to a velocity of 20 m/s in 10 seconds.

### Step 1: Identify the given values
- Mass (m) = 50 kg
- Initial velocity (u) = 0 m/s (since the body is at rest)
- Final velocity (v) = 20 m/s
- Time (t) = 10 s

### Step 2: Calculate the acceleration (a)
Using the formula for acceleration:
\[ a = \frac{v - u}{t} \]
Substituting the values:
\[ a = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = \frac{20 \, \text{m/s}}{10 \, \text{s}} = 2 \, \text{m/s}^2 \]

### Step 3: Calculate the force (F)
Using Newton's second law:
\[ F = m \cdot a \]
Substituting the values:
\[ F = 50 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 100 \, \text{N} \]

### Step 4: Calculate the displacement (s)
Using the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the values:
\[ s = 0 \cdot 10 + \frac{1}{2} \cdot 2 \, \text{m/s}^2 \cdot (10 \, \text{s})^2 \]
\[ s = 0 + \frac{1}{2} \cdot 2 \cdot 100 = 100 \, \text{m} \]

### Step 5: Calculate the work done (W)
Using the formula for work done:
\[ W = F \cdot s \]
Substituting the values:
\[ W = 100 \, \text{N} \cdot 100 \, \text{m} = 10000 \, \text{J} \]

### Final Answer
The work done to accelerate the body is **10000 Joules**.

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