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 to accelerate it from rest to 20 m/s in 10 seconds, we can follow these steps:

### Step 1: Identify the initial and final velocities
- The initial velocity (u) of the body is 0 m/s (since it starts from rest).
- The final velocity (v) of the body is 20 m/s.

### Step 2: Calculate the mass of the body
- The mass (m) of the body is given as 50 kg.

### Step 3: Use the formula for kinetic energy
The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]

### Step 4: Substitute the values into the kinetic energy formula
- Substitute m = 50 kg and v = 20 m/s into the formula:
\[ KE = \frac{1}{2} \times 50 \times (20)^2 \]

### Step 5: Calculate the final kinetic energy
- First, calculate \( (20)^2 \):
\[ (20)^2 = 400 \]
- Now substitute back into the equation:
\[ KE = \frac{1}{2} \times 50 \times 400 \]
\[ KE = 25 \times 400 \]
\[ KE = 10000 \text{ Joules} \]

### Step 6: Conclusion
The work done (W) by the force on the body is equal to the change in kinetic energy. Since the initial kinetic energy is 0 (the body starts from rest), the work done is:
\[ W = KE_{final} - KE_{initial} \]
\[ W = 10000 - 0 = 10000 \text{ Joules} \]

Thus, the work done by the force on the body is **10000 Joules**.

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