Question

A particle is moving along x-axis ,the acceleration in terms of x-coordinate x is given by a=-9*x, where x is in metre and a is in m/s^2 . Take the acceleration , velocity and displacement in positive x -direction as positive .The initial velocity of particle at x= 0 is u=+6m/s .the velocity of particle at x=2m wil be??

Answer 1

Dear Student
$$\begin{gathered} a=\frac{dv}{dt}=-9x \\ v=\frac{-9x^2}{2}+C \\ Atx=0,u=6m/s \\ 6=0+C \\ C=6 \\ Sovatx=2m \\ v=\frac{-9x^2}{2}+C=\frac{-9\times 2\times 2}{2}+6=-12m/s \end{gathered}$$
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