A vehicle starts from rest and accelerates al | vedclass

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(A) Let $v_s = 0$ be the speed of the source (siren) and $v_o$ be the speed of the observer (vehicle). The frequency heard by the observer is given by

Vedclass · Accepted Answer

$98$

Vedclass · Answer

(A) Let $v_s = 0$ be the speed of the source (siren) and $v_o$ be the speed of the observer (vehicle). The frequency heard by the observer is given by the Doppler effect formula: $f' = f_0 \left( \frac{v - v_o}{v} ight)$, where $v = 330 \,m/s$ is the speed of sound.Given $f' = 0.94 f_0$, we have $0.94 = \frac{330 - v_o}{330}$.Solving for $v_o$: $330 	imes 0.94 = 330 - v_o \implies 310.2 = 330 - v_o \implies v_o = 19.8 \,m/s$.The vehicle starts from rest $(u = 0)$ with acceleration $a = 2 \,m/s^2$. Using the equation of motion $v_o^2 = u^2 + 2as$:$(19.8)^2 = 0^2 + 2(2)s \implies 392.04 = 4s$.$s = \frac{392.04}{4} = 98.01 \,m$.Thus, the vehicle has gone nearly $98 \,m$.

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