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. 98m
C. 147m
D. 196m

Answer

B

Explanation

For motorcycle, `u = 0` and `a = 2 m//s^2` .
Observer is in motion and source is at rest.
`implies n' = n(v - v_0)/(v + v_s) implies 94/100 n = n = (330 - v_0)/(330) implies 330 - v_(0) = (330 xx 94)/100`
`implies v_(0) = 330 - (94 xx 33)/(10) = (33 xx 6)/(10) m//s`
Also, `s = (v^2 - u^2)/(2a) = (9 xx 33 xx 33)/(10) = (9 xx 1089)/(10) = 98m`.