Question

$(v-t)$ graph of a particle moving along $x$-axis is given. Its velocity-position graph if it starts from origin is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$v=kt$ (From given graph)
$dx=ktdt\Rightarrow {\int }_0^{x}dx=k{\int }_0^{t}tdt$
$\Rightarrow x=\frac{k{t}^2}{2}$ and since$t=\frac{v}{k}$
$\Rightarrow x=\frac{k}{2}\times \frac{v^2}{k^2}$
$x=\frac{v^2}{2k}$
Since we obtained a parabolic equation.
So, the correct option is $\left(b\right)$