First slide

Rectilinear Motion

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

Moderate

A

2/5
B

3/5
C

4/7
D

5/7

Solution

$\begin{array}{l} \frac{v_{av}}{v_{max}} = \frac{Total displacement}{2 (\begin{array}{l} Total displacement \\ during acceleration \\ and retardation \end{array}) + (\begin{array}{l} Displacement \\ during uniform \\ velocity \end{array})} \\ \frac{v_{av}}{v_{max}} = \frac{8 S}{2 (S + 5 S) + 2 S} = \frac{8}{14} = \frac{4}{7} \end{array}$

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