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 / meter during its travel from $x=20$ meter to $x=30$ meter. Its final kinetic energy will be

• A. $475J$
  
• B. $450J$
  
• C. $250J$
  
• D. $350J$
  

Answer 1

The correct option is A $475J$

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

Initial velocity $u=10m/s$

By third equation of motion

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

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

$\Rightarrow v^2=95$

$\Rightarrow K{E}_{final}=0.5\times m{v}^2=0.5\times 10\times 95=475J$

Hence correct answer is option $A$