Question

An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest?

Answer 1

Given:

Mass of object: \( m \) 
Velocity of object: \( v \)

Concept:

The work done to bring a moving object to rest is equal to the kinetic energy of the object: \[ W = \text{K.E.} = \frac{1}{2} m v^2 \]

Explanation:

- Kinetic energy of an object moving at velocity \( v \) is \( \frac{1}{2} m v^2 \).
- To stop the object, this energy must be removed by doing negative work (opposite to the motion).
- Therefore, the work done to bring the object to rest: \[ W = \frac{1}{2} m v^2 \]

Answer:

Work required to bring the object to rest = \( \frac{1}{2} m v^2 \) Joules