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. `98m`
B. `147m`
C. `96m`
D. `49m`

Answer

A

Explanation

Here, motor cyclist (i.e., listener) is moving away from source of sound (i.e., siren) at rest. Therefore,
`(v^('))/(v)=(upsilon-upsilon_(L))/(upsilon)=(94)/(100)` or `1-(upsilon_(L))/(upsilon)=(94)/(100)`
or`(upsilon_(L))/(upsilon)=1-(94)/(100)=(6)/(100)`
or `upsilon_(L)=(6xxupsilon)/(100)=(6xx330)/(100)=19.8m//s`
Distance covered, `S=(upsilon_(L)^(2))/(2a)=((19.8)^(2))/(2xx2)=98.01m`