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 : (A) 2 m/s2 (B) 4 m/s2 (C) 8 m/s2 (D) zero

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/576e892d8dab857fbde50be060fa6308-.png" /> From graph, x = Slope (t2) x =(2-0/1-0)(t2) x =2 t2 (d x/d t) =4 t (d2 x/d t2) =4 a =4 m / s 2 [∵ (d2 X/d t2)=a]

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

$2 m / s^{2}$

$4 m / s^{2}$

$8 m / s^{2}$

zero

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

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

2m/s2

4m/s2

8m/s2