Question 2: Motion in 1D

Question

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

Accepted Answer

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 $$t$$
$$\frac{d v}{d t}=-\frac{v_0}{x_0} \frac{d x}{d t}+0$$
or $$\quad a=-\frac{v_0}{x_0} v$$ ...... (ii)(
Putting $$v$$ from Eq. (i) in Eq. (ii),
$$\begin{aligned}
a & =-\frac{v_0}{x_0}\left[-\frac{v_0}{x_0} x+v_0ight] \
& =\frac{v_0^2}{x_0^2} x-\frac{v_0^2}{x_0}
\end{aligned}$$
Which represents a straight line with positive slope and negative intercept.

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Motion in 1D

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

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