Question

A block of mass 15 kg moving along x direction at a constant speed of 20${ms}^{-1}.$ It is subjected to a retarding force $F=2xJ{m}^{-1}$ during its journey from $x=10$ m to $x=40m.$ Its final kinetic energy will be:

• A. 500 J
• B. 1000 J
• C. 1500 J
• D. 2000 J

Answer 1

The correct option is C 1500 J

Let workdone by retarding force be $w$

$dw=dx=-2xdx$

$w=-{\int }_{10}^{40}2xdx$

$w={\frac{2\left[x^2\right]}{2}}_{10}^{40}=[1000-100]$

$w=-1500J$

Applying work energy theorem

$-w=K_f-K_i$

$\Rightarrow -1500+\left(\frac{1}{2}mV{i}^2\right)=k_f=-1500+\frac{1}{2}\times 15x\left(400\right)$

$\therefore k_f=1500g$

Here we work means force and displacement are opposite