The velocity v of a particle moving along x-axis varies with its position (x) as v=α √x ; where α is a constant. Which of the following graph represents the variation of its acceleration (a) with time (t) ?

Question

The velocity v of a particle moving along x-axis varies with its position (x) as v=α √x ; where α is a constant. Which of the following graph represents the variation of its acceleration (a) with time (t) ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

v=α √x Squaring both sides v2=α2 x Comparing above equation with 3 text rd equation of kinematics. v2=u2+2 a x α2 x=2 a x <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/94baf5c797e5307d3c69697d27b20757-.png" />

Q. The velocity $v$ of a particle moving along $x$ -axis varies with its position $(x)$ as $v = α x;$ where $α$ is a constant. Which of the following graph represents the variation of its acceleration $(a)$ with time $(t)$ ?

$v = α x$
Squaring both sides $v^{2} = α^{2} x$
Comparing above equation with $3^{rd}$ equation of kinematics.
$v^{2} = u^{2} + 2 a x$
$α^{2} x = 2 a x$

Q. The velocity v of a particle moving along x-axis varies with its position (x) as v=αx​; where α is a constant. Which of the following graph represents the variation of its acceleration (a) with time (t) ?

v=αx​ Squaring both sides v2=α2x Comparing above equation with 3rd equation of kinematics. v2=u2+2ax α2x=2ax

Q. The velocity $v$ of a particle moving along $x$ -axis varies with its position $(x)$ as $v = α x;$ where $α$ is a constant. Which of the following graph represents the variation of its acceleration $(a)$ with time $(t)$ ?

$v = α x$
Squaring both sides $v^{2} = α^{2} x$
Comparing above equation with $3^{rd}$ equation of kinematics.
$v^{2} = u^{2} + 2 a x$
$α^{2} x = 2 a x$