Question

A particle is moving along the xaxis whose instantaneous speed is given by v²=108-9x². find the acceleration of the particle.

(please give the answer with appropriate steps)​

Answer 1

please see the attachments

Answer 2

The acceleration of the particle (-9x) m/s².

Explanation:

A particle is moving along the x axis whose instantaneous speed is given by:

$v^2=108-9x^2$ .......(1)

Since,

$\dfrac{dx}{dt}=v\\\\\dfrac{dv}{dt}=a$

Differentiate equation (1) wrt t.

$2v\dfrac{dv}{dt}=0-18x{\cdot} \dfrac{dx}{dt}\\\\2v\times a=-18x{\cdot} v\\\\a=-9x$

The acceleration of the particle (-9x) m/s².

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Kinematics

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