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Question

A block of mass 10 kg is moving in x - direction with a constant speed of 10 m/s. It is subjected to a retarding force F=0.1x joule/metre during its travel from x=20 metre to x=30 metre. Its final kinetic energy will be

A
475 joule
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B
450 joule
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C
275 jolule
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D
250 jolule
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Solution

The correct option is A 475 joule
We know that,
Change in kinetic energy
= work done on the object by force
Here, work done = Fdx=30200.1x dx
=0.1[x22]3020=0.12[302202]
=0.5[900400]=0.05×500=25 Joule
Now, initial kinetic energy
=12×10×100=500 Joule
Final kinetic energy =50025=475 Joule

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