A vehicle starts from rest and accelerates along straight path at 2 ~m / s ^2 . At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at 94 % of its value when the vehicle was at rest? (speed of sound =330 ~m / s )

Step-by-step solution

The vehicle's speed when the driver hears the siren at 94% of its original frequency is determined from the Doppler effect for a moving observer receding from a stationary source: f' = f ( v_s - v_o v_s ) . Given f' = 0.94f and v_s = 330 , m/s , solve for v_o : 0.94 = 330 - v_o 330 v_o = 330 - 0.94 330 = 19.8 , m/s With constant acceleration a = 2 , m/s ^2 from rest, the distance traveled to reach this velocity is found from v^2 = u^2 + 2ax : 19.8^2 = 0 + 2 2 x 392.04 = 4x x = 98.01 , m Rounding to the nearest mete