A body of mass 2 kg is moving with a velocity of 5 m/s. How much work is required to stop the body?
Show Hint
- 10 J
- 15 J
- 20 J
- 25 J
The Correct Option is D
Solution and Explanation
To determine the work necessary to halt a moving object, one must quantify the alteration in its kinetic energy. The kinetic energy (\(KE\)) of an object is defined by the equation:
\( KE = \frac{1}{2}mv^2 \)
Here, \(m\) represents the object's mass and \(v\) denotes its velocity.
Provided data:
- Mass (\(m\)) = 2 kg
- Velocity (\(v\)) = 5 m/s
Substituting the provided values into the formula yields:
\( KE = \frac{1}{2} \times 2 \, \text{kg} \times (5 \, \text{m/s})^2 \)
\( KE = 1 \times 25 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \)
\( KE = 25 \, \text{J} \)
The initial kinetic energy of the object is 25 J. As the objective is to stop the object, its final kinetic energy will be 0 J. The work expended to cease the object's motion is equivalent to the inverse of its initial kinetic energy (indicating dissipation):
Work Done = \(- \text{Initial KE} = -25 \, \text{J}\)
Consequently, 25 J of work is required to bring the object to a standstill.
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