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

Options

A. `2//5`
B. `3//5`
C. `4//5`
D. `6//7`

Answer

B

Explanation

`V_(av) = (x + 2x + 3x)/(t_(1) + t_(2) + t_(3))`
`t_(1) = (2x)/(v_("max")), t_(2) = (2x)/(v_("max")), t_(3) = (6x)/(v_("max))`
`v_(av) = (6 x v_("max"))/(10x) rArr (v_(av))/(v_("max")) = (3)/(5)`