A person has a box of weight 20 kg. The energy of the box, wihen the person runs with a constanL velocity of 2 `ms^(-1)` along with the box behind the bus, is given as

Options

A. 20 J
B. 40 J
C. 80 J
D. zero

Answer

To solve the problem, we need to calculate the kinetic energy of the box when the person runs with it at a constant velocity. The formula for kinetic energy (KE) is given by:

\[ KE = \frac{1}{2} mv^2 \]

Where:
- \( m \) is the mass of the object (in kilograms)
- \( v \) is the velocity of the object (in meters per second)

### Step 1: Identify the mass of the box
The weight of the box is given as 20 kg. Therefore, we have:
\[ m = 20 \, \text{kg} \]

### Step 2: Identify the velocity of the box
The velocity at which the person is running with the box is given as:
\[ v = 2 \, \text{m/s} \]

### Step 3: Substitute the values into the kinetic energy formula
Now we can substitute the values of \( m \) and \( v \) into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 20 \, \text{kg} \times (2 \, \text{m/s})^2 \]

### Step 4: Calculate the square of the velocity
Calculating \( (2 \, \text{m/s})^2 \):
\[ (2 \, \text{m/s})^2 = 4 \, \text{m}^2/\text{s}^2 \]

### Step 5: Substitute the squared velocity back into the kinetic energy formula
Now substituting back:
\[ KE = \frac{1}{2} \times 20 \, \text{kg} \times 4 \, \text{m}^2/\text{s}^2 \]

### Step 6: Perform the multiplication
Calculating the kinetic energy:
\[ KE = \frac{1}{2} \times 20 \times 4 = 10 \times 4 = 40 \, \text{Joules} \]

### Final Answer
The energy of the box when the person runs with a constant velocity of 2 m/s is:
\[ \text{Kinetic Energy} = 40 \, \text{Joules} \]