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Work, Energy And Power

Question
CBSEENPH11020528
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A block of mass 10 kg, moving in the x-direction with a constant speed of 10 ms-1 , is subjected to a retarding force F= 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be

  • 475 J

  • 450 J

  • 275 J

  • 250 J 

Solution

A.

475 J

From work energy theorem
work done = change in KE
⇒ W = Kf -Ki
rightwards double arrow space straight K subscript straight f end subscript space equals space straight W space plus straight K subscript straight i space end subscript equals space integral subscript straight x subscript 1 end subscript superscript straight x subscript 2 end superscript Fxdx space plus 1 half mv squared equals integral subscript 20 superscript 30 minus 0.1 space straight x space dx space plus 1 half space straight x space 10 space straight x space space 10 squared space equals space minus 0.1 open square brackets straight x squared over 2 close square brackets subscript 20 superscript 30 space plus 500 equals negative 0.50 left square bracket 30 squared minus 20 squared right square bracket space plus 500 equals negative 0.05 left square bracket 900 minus 400 right square bracket plus 500 rightwards double arrow space straight K subscript straight f equals negative 25 plus 500 equals 475 space straight J

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