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

Answer

A

Explanation

Motor cycle has travlleed a distance `s`. Its velocity at that point
`v = sqrt(2as)`
The observed frequency
`f' = f''=(330 - v)/(330)`
`rArr 0.94 = (330 - v)/(330) rArr v = 0.06 xx 330 m//s = 19.8 m//s`
`s = (v^(2))/(2a) = (19.8^(2))/(2 xx 2) = 9.9^(2) = 98 m`