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 $x=20m$ to $x=30m$. Its final kinetic energy will be (in $J$)

• A. $475$
  
• B. $450$
  
• C. $275$
  
• D. $250$
  

Answer 1

Answer: (A)

$475$

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 $A$