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A motor cycle starts from rest and accelerates along a straight path at 2 m/s². At the straight 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 = 330 ms^-1)

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98 m

147 m

49 m

196 m

answer is A.

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Detailed Solution

$n^{1} = n [\frac{v}{v - v_{0}}]; \frac{94}{100} n = n [\frac{v}{v - v_{0}}]$

$v_{o} = \frac{6}{100} 330 = 19.8 m / s$

$\Rightarrow$ v₀² - 0² = 2as
$s = \frac{{v_{0}}^{2}}{2 a} = 98 m$

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