Question

A body of mass 2 kg is moving with a velocity of 5 m/s. How much work is required to stop the body?

• A. 10 J
• B. 15 J
• C. 20 J
• D. 25 J

Hint:

Tip: Work done to stop a moving body is equal to its initial kinetic energy.

Answer 1

The Correct Option is D

To calculate the work required to stop a moving body, we need to determine the change in its kinetic energy. The kinetic energy (\(KE\)) of a body is given by the formula:

\( KE = \frac{1}{2}mv^2 \)

where \( m \) is the mass of the body and \( v \) is its velocity.

Given:

• Mass (\( m \)) = 2 kg
• Velocity (\( v \)) = 5 m/s

Substitute the given values into the formula:

\( KE = \frac{1}{2} \times 2 \, \text{kg} \times (5 \, \text{m/s})^2 \)

\( KE = 1 \times 25 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \)

\( KE = 25 \, \text{J} \)

The initial kinetic energy of the body is 25 J. Since the body is required to be stopped, its final kinetic energy will be 0 J. The work done to stop the body will be equal to the negative of the initial kinetic energy (as it needs to be fully dissipated):

Work Done = \(- \text{Initial KE} = -25 \, \text{J}\)

Thus, 25 J of work is required to stop the body.

Answer 2

Step 1: Use the work-energy principle. 
The work required to stop the body equals the loss in kinetic energy.

Step 2: Calculate initial kinetic energy. 
\[ KE = \frac{1}{2} m v^2 = \frac{1}{2} \cdot 2 \cdot (5)^2 = 25 \text{ J} \]

Step 3: Final velocity is 0, so all kinetic energy is lost. 
Hence, work done to stop the body = \( \boxed{25 \text{ J}} \)