1. Tardigrade
  2. Question
  3. Physics
  4. A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance of 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A person pushes a box on a rough horizontal platform surface. He applies a force of $200\, N$ over a distance of $15\, m$. Thereafter, he gets progressively tired and his applied force reduces linearly with distance of $100\, N$. The total distance through which the box has been moved is $30 m$. What is the work done by the person during the total movement of the box?

JEE MainJEE Main 2020Work, Energy and Power

Solution:

$F =200 \,N \,\,\,\,\,\,\,$ for $0 \leq x \leq 15$
$=200-\frac{100}{15}( x -15)$ for $\,\,\,\,\,\, 15 \leq x <30$
$W =\int F \, dx$
$=\int\limits_{0}^{15} 200 \,dx +\int\limits_{15}^{30}\left(300-\frac{100}{15} x \right) dx$
$=200 \times 15+300 \times 15-\frac{100}{15} \times \frac{\left(30^{2}-15^{2}\right)}{2}$
$=3000+4500-2250$
$=5250 \,J$