Question

A particle starts from east and travels a distance $S$ with uniform acceleration, then it travels a distance $2S$ with uniform speed, finally it travels a distance $3S$ with uniform retardation and comes to rest. If the complete motion of the particle is a straight line then the ratio of its average to maximum velocity is:

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

Answer 1

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

(i) for $1^{st}$ part
$S=\left(\frac{0+v_{max}}{2}\right)t_1=\frac{v_{max}}{2}{t}_1$
$\therefore t_1=\frac{2s}{v_{max}}$
(ii)$t_2=\frac{2s}{v_{max}}$ as it moves with constant velocity
(iii) For this part
$3S=\left(\frac{0+v_{max}}{2}\right)t_3=\frac{v_{max}}{2}or{t}_3=\frac{6s}{v_{max}}$
Now average velocity
$\overline{v}=\frac{s+2s+3s}{\frac{2s}{v_{max}}+\frac{2s}{v_{max}}+\frac{6s}{v_{max}}}=\frac{6}{10}{v}_{max}$
$\Rightarrow \frac{\overline{v}}{v_{max}}=\frac{3}{5}$