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

Question

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" /> (A) 4ms- 2 (B) 8ms- 2 (C) Zero (D) 2ms- 2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-kepdftrbtgoeweau.jpg" /> From the graph, x=( textSlope)× (.t2.) x=(2 - 0/1 - 0)(.t2.) x=2t2 (d x/d t)=4t (d2 x/d t2)=4 a=4ms- 2 [∵ (d2 x/d t2) = a]

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

$4 m s^{- 2}$

$8 m s^{- 2}$

Zero

$2 m s^{- 2}$

From the graph,
$x = (Slope) \times (t^{2})$
$x = \frac{2 - 0}{1 - 0} (t^{2})$
$x = 2 t^{2}$
$\frac{d x}{d t} = 4 t$
$\frac{d ^{2} x}{d t ^{2}} = 4$
$a = 4 m s^{- 2}$ $[∵ \frac{d ^{2} x}{d t ^{2}} = a]$

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

4ms−2

8ms−2