Question

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

• A. $250J$
• B. $325J$
• C. $625J$
• D. $475J$

Answer 1

The correct option is D $475J$

Initial velocity $u=10m/s$

Acceleration $=F/m=-0.1x/10=-0.01x$ $m/s^2$

Applying third equation of motion

$\Rightarrow v^2-u^2=2as$

$\Rightarrow v^2-100={\int }_{20}^{30}2(-0.01x)dx$

$\Rightarrow v^2-100=-0.01({30}^2-{20}^2)$

$\Rightarrow v^2=95$

Final KE $=0.5\times m{v}^2=0.5\times 10\times 95=475J$

Hence correct answer is option $D$