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The speed v of a particle moving along a straight line when it is at a distance  x from  a fixed point on the line is given by v2=1449x2. Select the correct alternatives

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a
The motion of the particle is SHM with time period T=2π3unit
b
The maximum displacement of the particle from the fixed point is 8 unit
c
The magnitude of the acceleration at a distance 3 unit from the fixed point is 24 unit
d
The motion of the particle is periodic but not simple harmonic

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detailed solution

Correct option is A

The equation resembles equation for velocity n SHM.Comparing with equation of SHM, v2=A2ω2−x2ω2 we get, ω=3,  A=4 .T=2πω=2π3  unitMaximum displacement = A = 4 unit. Hence option (B) is wronga=ω2x=9(3)=27 unit. Hence option (C) is wrongDifferentiating v2=144−9x2, we get a   α−x . This makes it simple harmonic  motion. Hence option (D) is wrong.


Similar Questions

A horizontal platform with an object placed on it is executing S.H.M. in the vertical direction. The amplitude of oscillation is 3.92×103m . What must be the least period of these oscillations, so that the object is not detached from the platform 


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