Question

A particle starting from rest moves along a straight line with uniform acceleration. Its kinetic energy is $K$ when its displacement is $s$. A graph is drawn between $K$ (on Y-axis) and $s$ (on X-axis). The shape of the graph is:

• A. a straight line not passing through the origin
• B. a parabola
• C. a straight line passing through the origin
• D. a rectangular hyperbola

Answer 1

Answer: (C)

a straight line passing through the origin

$v=at$
$s=\frac{1}{2}a{t}^2\Rightarrow t^2=\frac{2s}{a}\to \left(1\right)$
$KE=\frac{1}{2}m{v}^2=\frac{1}{2}m{a}^2{t}^2=K$
now
substituting from (1) $\Rightarrow mas=K$
As acceleration and mass are constant, we get a straight line graph between the $K$ and $s$.