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  4. Displacement x versus t2 graph is shown for a particle. The acceleration of the particle is :

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

UPSEEUPSEE 2017

Solution:

image
From graph,
x = Slope $\left(t^{2}\right) $
$x =\frac{2-0}{1-0}\left(t^{2}\right) $
$x =2 t^{2} $
$\frac{d x}{d t} =4 t $
$\frac{d^{2} x}{d t^{2}} =4$
$a =4 \,m / s ^{2}$
$[\because \frac{d^{2} X}{d t^{2}}=a]$