A block of mass 10kg is moving in x-direction with a constant speed of 10 m/s . It is subjected to a retarding force F=-0.1 x joule / meter during its travel from x=20 meter to x=30 meter. Its final kinetic energy will be.   Option 1) 475 J  Option 2) 450 J  Option 3) 275 J Option 4) 250 J

P Plabita

As we discussed in Concept

Net work done by all the forces give the change in kinetic energy -

$W=\frac{1}{2}mv^{2}-\frac{1}{2}mv{_{0}}^{2}$

$W= k_{f}-k_{i}$

- wherein

$m=mass \: of\: the\: body$

$v_{0}= initial\: velocity$

$v= final\: velocity$

$W=k_{f}-k_{i}$

$=> k_{f}=W+k_{i}$

$k_{f}=\int_{x_{1}}^{x_{2}}fxdx+\frac{1}{2}mv^{2}$

$=>\int_{30}^{20}-0.1\times dx+\frac{1}{2} 10\times 10^{2}$

$=-0.1\left [ \frac{x^{2}}{2} \right ]^{30}_{20}+500$

$=-0.50\left [ 30^{2}-20^{2} \right ]+500$

$=-0.05\left [ 900-400 \right ]+500$

$k_{f}=-25+500=475J$

Option 1)

475 J

Option is correct

Option 2)

450 J

Option is incorrect

Option 3)

275 J

Option is incorrect

Option 4)

250 J

Option is incorrect

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