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

As we discussed in

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

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

$v_{0}= initial\: velocity$

$v= final\: velocity$

Definition of work done by variable force -

$W=\int \vec{F}\cdot \vec{ds}$

- wherein

$\vec{F}$ is variable force and $\vec{ds}$ is small displacement

$k_{i}=\frac{1}{2}m{v_{i}}^{2}=\frac{1}{2}\times 10\times \left ( 10 \right )^{2}=500J$

w= $\int_{x_{1}}^{x_{2}}f_{r}.dx=\int_{20}^{30}-0.1x dx= -0.1\left [ \frac{x^{2}}{2} \right ]^{30}_{20}= -0.1\left [ \frac{900-400}{2} \right ]= -25J$

w= $k_{f}-k_{i}=k_{f}=w+k_{i}$

-25 J+500 J = 475 J

Option 1)

275 J

Incorrect Option

Option 2)

250 J

Incorrect Option

Option 3)

475 J

Correct Option

Option 4)

450 J

Incorrect Option

475J

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