Question

What will be the $a$ vs $x$ graph for the following graph?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Equation of given line when velocity is plotted against position with intercept $=v_0$ and slope $=v_0/x_0$ is,
$v=-\frac{v_{0}x}{x_0}+v_0$ ...(i)
(-Ve sign is became the slope is decreasing)
On differentiating with respect to $t$
$\frac{dv}{dt}=-\frac{v_0}{x_0}\frac{dx}{dt}+0$
or $a=-\frac{v_0}{x_0}v$ ...(ii)
Putting $v$ from Eq. (i) in Eq. (ii),
$a=-\frac{v_0}{x_0}\left[-\frac{v_0}{x_0}x+v_0\right]$
$=\frac{v_0^2}{x_0^2}x-\frac{v_0^2}{x_0}$
Which represents a straight line with positive slope and negative intercept.