Physics - W.E.P. Question with Solution | TestHub

f = a - bx

${\text{f}}_{{\text{n}}_{\text{ef}}}=\text{a}-\text{bx}-{\text{f}}_{\text{s}}$

For block to move

at x = 0

$\text{a}-{\text{b}}_{\text{x}}>{\left({\text{f}}_{\text{s}}\right)}_{\text{max}}=\mu \text{mg}$

$\text{a}>\mu \text{mg}$, So we are assuming motion starts at x = 0

$\text{w}=\int \left(\text{a}-\text{bx}-\mu \text{mg}\right)\text{dx}$

$\text{o}=\text{ax}-\frac{{\text{bx}}^2}{2}-\mu \text{mgx}$

$\Rightarrow \text{x}\left(\text{a}-\frac{\text{bx}}{2}-\mu \text{mg}\right)=0$

x = 0

$\text{a}-\frac{\text{bx}}{2}-\mu \text{mg}=0$

$\frac{\text{bx}}{2}=\left(\text{a}-\mu \text{mg}\right)$

$\text{x}=\frac{2}{\text{b}}\left(\text{a}-\mu \text{mg}\right)$