Question:
A person pushes a box on a rough horizontal plateform 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 to 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?
A person pushes a box on a rough horizontal plateform 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 to 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?
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Work is the area under the F-x graph: a rectangle for the first 15 m and a trapezoid for the next 15 m.
Updated On: Nov 5, 2026
- 5690 J
- 5250 J
- 2780 J
- 3280 J
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The Correct Option is B
Solution and Explanation
First 15 m: force is constant at 200 N, so \(W_1 = 200\times15 = 3000\) J.
Next 15 m (x = 15 m to 30 m): force falls linearly from 200 N to 100 N. \(F = 200 - \dfrac{100}{15}(x - 15)\).
\(W_2 = \int_{15}^{30}F\,dx = \dfrac{200+100}{2}\times15 = 2250\) J.
Total \(W = 3000 + 2250 = 5250\) J.
Answer: (2) 5250 J
Next 15 m (x = 15 m to 30 m): force falls linearly from 200 N to 100 N. \(F = 200 - \dfrac{100}{15}(x - 15)\).
\(W_2 = \int_{15}^{30}F\,dx = \dfrac{200+100}{2}\times15 = 2250\) J.
Total \(W = 3000 + 2250 = 5250\) J.
Answer: (2) 5250 J
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