Question

A body starts from rest and travels a distance S with uniform acceleration, then moves uniformly a distance 2S and finally comes to rest after moving further 5S under uniform retardation. The ratio of the average velocity to maximum velocity is

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

Answer 1

Answer: (C)

Graphically, the area of v-t curve represents displacement:
$S=\frac{1}{2}\,v_{max} \,t_{1}\quad or\quad t_{1}\,=\frac{2S}{v_{max}}$
$2S=v_{max}\,t_{2}\quad or\quad t_{2}=\frac{2S}{v_{max}};$
$5S=\frac{1}{2}\,v_{max} \,t_{3}\quad or\quad t_{3}\,=\frac{10S}{v_{max}}$
$v_{av}=\frac{Total displacement}{Total time}$
$=\frac{S+2S+5S}{\frac{2S}{v_{max}}+\frac{2S}{v_{max}}+\frac{10S}{v_{max}}}$
$\frac{v_{av}}{v_{max}}=\frac{8S}{14S}=\frac{4}{7}$