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A block of mass 10 kg, moving in x direction with a constant speed of 10 m/s, is subject to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be:

1. 450 J
2. 275 J
3. 250 J
4. 475 J

Correct answer: 250 J

Solution

The work done by the retarding force is calculated as the integral of F over the distance (20 m to 30 m). This work reduces the initial kinetic energy of the block. Initial KE = 0.5 * 10 * (10)^2 = 500 J. Work done = ∫(0.1x dx) from 20 to 30 = [0.05x^2] from 20 to 30 = 0.05(30^2 - 20^2) = 25 J. Final KE = Initial KE - Work done = 500 - 25 = 250 J.

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