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  • A body starts from origin moves along the x axis such that the velocity at any instant is given by( 4t^3-2t) .what is the acceleration of the particle when it is at a distance 2 meter from the origin?

A body starts from origin moves along the x axis such that the velocity at any instant is given by( 4t^3-2t) .what is the acceleration of the particle when it is at a distance 2 meter from the origin?

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\begin{array}{l} v=4 t^{3}-2 t \text { (given) }\\ a=\frac{d v}{d t}=12 t^{2}-2 \\ \text { and } x=\int_{0}^{t} v d t=\int_{0}^{t}\left(4 t^{3}-2 t\right) d t =t^{4}-t^{2} \end{array}

When a particle is at 2 m from the origin

t^{4}-t^{2}=2 \Rightarrow t^{4}-t^{2}-2=0\\\Rightarrow \left(t^{2}-2\right)\left(t^{2}+1\right)=0 \Rightarrow t=\sqrt{2} \mathrm{sec}

acceleration \ \ at\ \ t=\sqrt{2}$ sec \\ given by $a=12 t^{2}-2=12 \times 2-2=22 \frac{m}{s^{2}}$

Posted by

avinash.dongre

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