For a particle under going rectilinear motion with uniform acceleration, the magnitude of displacement is one third the distance covered in some time interval. The magnitude of final velocity is less than magnitude of initial velocity for this time interval. Then the ratio of initial speed velocity to the final speed for this time interval is :

Options

A. `sqrt(2)`
B. 2
C. `sqrt(3)`
D. 3

Answer

A

Explanation

Let `u` and `v` denote initial and find velocity then nature of motion is indicated in diagram
.
Hence initial and final speed are given by equation
`O_(2)=u_(2) -2a xx 2S` and `v_(2) =0_(2) + 2as`
`:. V=(u)/(sqrt(2))` or `(u)/(v)=sqrt(2)` .