A motor cycle starts from rest and accelerates along a straight...

A motor cycle starts from rest and accelerates along a straight path at

2 \mathrm{~m} / \mathrm{s}^2

. At the starting point of the motor cycle there is a stationary electric sire. 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

\left.=330 \mathrm{~ms}^{-1}\right)

Options

A $49 \mathrm{~m}$
B $98 \mathrm{~m}$
C $147 \mathrm{~m}$
D $196 \mathrm{~m}$

Correct answer

B. $98 \mathrm{~m}$

Step-by-step solution

Motor cycle,

u=0, a=2 \mathrm{~m} / \mathrm{s}^2

Observer is in motion and source is at rest.

\begin{aligned}& \Rightarrow n^{\prime}=n \frac{v-v_O}{v+v_S} \Rightarrow \frac{94}{100}n=n \frac{330-v_O}{330} \Rightarrow330-v_0=\frac{330 \times 94}{100}\\ & \Rightarrow v_O=330-\frac{94 \times 33}{10}=\frac{33 \times 6}{10} \mathrm{~m}/ \mathrm{s}\\ & s=\frac{v^2-u^2}{2 a}=\frac{9 \times 33 \times 33}{100}=\frac{9 \times 1089}{100} \approx98 \mathrm{~m} . \end{aligned}

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