How much work must work be done by a force on 50 kg body in order to accelerate it in the direction of force from rest to `20 ms^(-1)` is 10 s?

Options

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

Explanation

To solve the problem of how much work must be done by a force on a 50 kg body in order to accelerate it from rest to 20 m/s in 10 seconds, we can follow these steps:

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

### Step 2: Calculate the acceleration
Using the equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ 20 = 0 + a \cdot 10 \]
To find acceleration (a):
\[ a = \frac{20}{10} = 2 \, \text{m/s}^2 \]

### Step 3: Calculate the displacement
Using the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ s = 0 \cdot 10 + \frac{1}{2} \cdot 2 \cdot (10)^2 \]
\[ s = 0 + \frac{1}{2} \cdot 2 \cdot 100 \]
\[ s = 100 \, \text{m} \]

### Step 4: Calculate the work done
Work done (W) is given by the formula:
\[ W = F \cdot s \cdot \cos(\theta) \]
Since the force is applied in the direction of displacement, \(\theta = 0\) and \(\cos(0) = 1\):
\[ W = F \cdot s \]
From Newton's second law, force (F) can be calculated as:
\[ F = m \cdot a \]
Substituting the values:
\[ F = 50 \cdot 2 = 100 \, \text{N} \]
Now substituting back into the work done formula:
\[ W = 100 \cdot 100 \]
\[ W = 10,000 \, \text{J} \]

### Final Answer
The work done by the force is **10,000 Joules**.

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