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

Answer

D

Explanation

Motor cycle, u = 0, `a = 2 m//s^(2)`
Observer is in motion and source is at rest.
f' is the appeared frequency
`f' = ((upsilon - upsilon_(0))/(upsilon - (-upsilon_(S))))f = ((330 - upsilon_(0))/(330))f`
`rArr" "(f')/(f) = ((330 - upsilon_(0))/(330))`
`(0.94 f)/(f) = (330 - upsilon_(0))/(330)`
`upsilon_(0) = 19.8 m//s ~~ 20 m//s`
The distance of motor cycle is
`S = (upsilon_(0)^(2) - u^(2))/(2a) = ((19.8)^(2) - 0)/(4) = 98` m