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

B

Explanation

`(n_(a))/(n) = 0.94 n_(a) = ((V - V_(S))/(V))n`
`:. 0.94 = 1 - (V_(S))/(V)`
`:. (V_(S))/(V) = 1 - 0.94 = 0.06`
`:. V_(s) = 330 xx 0.06 = 19.8m//s`
Using `v^(2) = u^(2) + 2as " " u =0, a = 2 m//s`
`:. 19.8 xx 19.8 = 2 xx 2 s`
`:. s = 98 m`