A motor cycle starts from rest and accelerates along a straight path at `2m//s^(2)`. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at `94%` of its value when the motor cycle was at rest ? (Speed of sound = `330ms^(-2))`

Options

A. 49 m
B. 98 m
C. 147 m
D. 196 m

Answer

D

Explanation

Here, the source (electric siren) is at rest and the observer is moving away from the source.
`therefore upsilon.=(upsilon(v-v_(o)))/(v)or(upsilon.)/(upsilon)=(v-v_(o))/(v)`
or `(94)/(100)=1-(v_(o))/(v)`
or `0.94=1-(v_(o))/(v)or(v_(o))/(v)=1-0.94=0.06`
or `v_(o)=0.06v=0.06xx330=19.8ms^(-1)`
`therefore` Distance covered. `s=(v^(2)-u^(2))/(2a)=((19.8)^(2)-(0)^(2))/(2xx2)~~98m`