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A motor cycle starts from rest and accelerates along a straight path at 2 m/s². 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 = 330 m s⁻¹)

1. 98 m
2. 147 m
3. 196 m
4. 49 m

Correct answer: 98 m

Solution

The motorcycle accelerates and approaches the stationary siren, causing a Doppler effect that shifts the frequency heard by the driver. When the frequency is perceived at 94% of its original value, the motorcycle's speed relative to the sound wave allows us to calculate the distance traveled using the relationship between speed, acceleration, and time.

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