Question

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

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

Answer 1

Answer: (D)

$\frac{6}{7}$

let acceleration is $a.$ then

for first x distance. using equation of motion for constant acceleration

$v=\sqrt{2ax}$ and time taken to cover this distance is $T_1=\sqrt{\frac{2x}{a}}$

for second 2x distance

time taken to cover is $T_2=\frac{2x}{\sqrt{2ax}}$ then $T_2=\sqrt{\frac{2x}{a}}$

for 3rd diatnce of 3x

$a_2=\frac{2ax}{3x}$. then $T_3=\frac{\sqrt{2ax}}{\frac{2a}{3}}$ then total time is $T=(\frac{3}{2}+1+1)\sqrt{\frac{2x}{a}}$

average velocity is $\frac{6x}{\frac{7}{2}.\sqrt{\frac{2x}{a}}}.$ $=>V_{Av}=\frac{6}{7}.\sqrt{2ax}$.

then ration of average velocity to maximum velocity is $\frac{6}{7}$.