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  4. Displacement x versus t2 graph is shown for a particle. The acceleration of the particle is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-kepdftrbtgoed0kq.jpg />

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Q. Displacement $x$ versus $t^{2}$ graph is shown for a particle. The acceleration of the particle is
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
From the graph,
$x=\left(\text{Slope}\right)\times \left(\right.t^{2}\left.\right)$
$x=\frac{2 - 0}{1 - 0}\left(\right.t^{2}\left.\right)$
$x=2t^{2}$
$\frac{d x}{d t}=4t$
$\frac{d^{2} x}{d t^{2}}=4$
$a=4ms^{- 2} \, $ $\left[\because \, \, \, \frac{d^{2} x}{d t^{2}} = a\right]$