Work is calculated using the formula:
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
where:
- Work is measured in joules (J),
- Force is measured in newtons (N),
- Distance is measured in meters (m),
- \(\theta\) is the angle between the force and the direction of movement.
In this case, the person applies a force of 400 newtons over a distance of 4 meters in the same direction as the force, so \(\theta = 0\) degrees. Thus, \(\cos(0) = 1\).
The work done by the person while pushing the box can be calculated as:
\[ \text{Work} = 400 , \text{N} \times 4 , \text{m} \times 1 = 1600 , \text{J} \]
After the person stops pushing, the box slides forward an additional meter due to its inertia. However, this distance does not contribute to the work done by the person, as it does not involve any force applied by the person.
Therefore, the total work done by the person is:
\[ \text{Total Work} = 1600 , \text{J} \]
So, the work done by the person is 1600 joules.