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A block of mass 10 kg, moving in x direction with a constant speed of 10 m$s^{-1}$, 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
A
475 J
B
450 J
C
275 J
D
250 J
Detailed Solution
Work done by the retarding force: $W = -\int_{20}^{30} 0.1x\,dx = -0.1\left[\frac{x^2}{2}\right]_{20}^{30} = -0.05(900 - 400) = -25$ J
Initial KE $= \frac{1}{2}\times 10\times 10^2 = 500$ J
By the work-energy theorem, $KE_{final} = KE_{initial} + W = 500 - 25 = 475$ J
Initial KE $= \frac{1}{2}\times 10\times 10^2 = 500$ J
By the work-energy theorem, $KE_{final} = KE_{initial} + W = 500 - 25 = 475$ J