Question

Block is projected with speed $v_0=12$ m/s, surface of ground is greasy, hence coefficient of friction varies as $\mu$=$6.4x$ , find distance covered by the block before it stops.

• A. $\frac{5}{6}$ m
• B. $\frac{4}{8}$ m
• C. $\frac{3}{2}$ m
• D. $\frac{7}{9}$ m

Answer 1

The correct option is C $\frac{3}{2}$ m

$a=\frac{F}{m}=\frac{\mu \text{/}mg}{\text{/}m}=\mu g=\left(cx\right)g$

$a=-v\frac{dv}{dx}=cxg$

$\int vdv=-g\int cxdx$

${\int }_{v_0}^{0}vdv=-cg{\int }_0^{x}xdx$

$\frac{v_0^2}{2}=cg\frac{x^2}{2}$

$v_0^2=cg{x}^2$

$x=\sqrt{\frac{v_0^2}{cg}}=\sqrt{\frac{(12{)}^2}{6.4\times 10}}=\frac{12}{8}=1.5m$