Question

A body starts from rest and travels a distance S with uniform acceleration, then moves uniformly a distance 2S uniformly, 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. $\frac{5}{2}$

Answer 1

The correct option is C $\frac{4}{7}$

From the question a graph is drawn above,

Area of $v-t$ graph$⟹$ distance travelled

$v_{avg}=\frac{8s}{t_1+t_2+t_3}$

$\frac{1}{2}{v}_m\times t_1=s$

$t_1=\frac{2s}{v_m}$

$t_2\times v_m=2s$

$t_2=\frac{2s}{v_m}$

$\frac{1}{2}\times t_3\times v_m=5s$

$t_3=\frac{10s}{v_m}$

$v_{avg}=\frac{8s}{\frac{2s}{v_m}+\frac{2s}{v_m}+\frac{10s}{v_m}}$

$\frac{v_{avg}}{v_m}=\frac{4}{7}$