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

Options

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

Answer

C

Explanation

Maximum velocity `v_("max") = sqrt(2as)`
`V_("av") = (6s)/T T = t_(1) + t_(2) + t_(3)`
`t_(1) = sqrt((2s)/a), t_(2) = (2s)/v_("max") = sqrt((2s)/a)`
Retardation `rArr B`
`beta = v_("max")^(2)/(6s)`
`beta =(2a xx s)/(6 xx s) = a/3`
`t_(3) = v_("max")/beta = 3 sqrt((2a xx s)/a) = 3 sqrt((2s)a)`
`T = 5 sqrt((2s)/a)`
`v_("avg") = 6/5 5/sqrt((2s)/a)`
`v_("avg") = 6/5 sqrt((as)/2)`
`v_("avg")/v_("max") = 6/5 sqrt((as)/2) xx 1/sqrt((2as)) = 3/5`