How much work must be done by a force on 50 kg body in order to accelerate it from rest to 20m/s in 10s?

Options

A. `10^3 J`
B. `10^4 J`
C. `2 xx 10^3 J`
D. `5 xx 10^4 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: Determine the acceleration of the body
We know the initial velocity (u) is 0 m/s (since the body starts from rest), the final velocity (v) is 20 m/s, and the time (t) is 10 seconds. We can use the first equation of motion:

\[ v = u + at \]

Substituting the known values:

\[ 20 = 0 + a \cdot 10 \]

Solving for acceleration (a):

\[ a = \frac{20}{10} = 2 \, \text{m/s}^2 \]

### Step 2: Calculate the force acting on the body
Using Newton's second law, the force (F) can be calculated using the formula:

\[ F = m \cdot a \]

where m is the mass of the body (50 kg) and a is the acceleration we just calculated (2 m/s²):

\[ F = 50 \cdot 2 = 100 \, \text{N} \]

### Step 3: Calculate the displacement of the body
To find the displacement (s) during the acceleration, we can use the second equation of motion:

\[ s = ut + \frac{1}{2} a t^2 \]

Since the initial velocity (u) is 0:

\[ s = 0 \cdot 10 + \frac{1}{2} \cdot 2 \cdot (10)^2 \]

Calculating the displacement:

\[ s = \frac{1}{2} \cdot 2 \cdot 100 = 100 \, \text{m} \]

### Step 4: Calculate the work done by the force
The work done (W) is given by the formula:

\[ W = F \cdot s \]

Substituting the values of force and displacement:

\[ W = 100 \cdot 100 = 10,000 \, \text{J} \]

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

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