Question

A particle starts from rest and travels a distance d with uniform acceleration, then it travels a distance 2d with uniform speed and finally it travels a distance 3d with uniform retardatron to come to rest. Ratio of average velocity to maximum velocity is

• A. $\frac{2}{3}$
• B. $\frac{3}{5}$
• C. $\frac{5}{3}$
• D. $2$

Answer 1

The correct option is B $\frac{3}{5}$



$v^2=0^2+2ad$
$0^2=v^2-2a^{\prime }\times 3d$
$a^{\prime }=\frac{a}{3}<v>=\frac{6d}{t_1+t_2+t_3}where{t}_1=\frac{v}{a},t_2=\frac{2d}{v}and{t}_3=\frac{v}{a^{\prime }}=\frac{3v}{a}$
$\Rightarrow <v>=\frac{6d}{\frac{v}{a}+\frac{2d}{v}+\frac{3v}{a}}=\frac{6d}{\frac{v}{a}+\frac{2dv}{v^2}+\frac{3v}{a}}=\frac{6da}{5v}(\because v^2=2ad)=\frac{6}{5}\frac{v^2}{2v}=\frac{3}{5}v\Rightarrow \frac{<v>}{v}=\frac{3}{5}$