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This question, I solved quite theoretically differentiating the equation of given graph $$(v=mx+v_0)$$ taking $m$ as slope of given line. Note that $m$ is a non-zero negative number. Thus $$a=m^2x+mv_0$$ which means that acceleration as a function of distance when graphed should have a positive non-zero slope and a negative y intercept (because $m$ is negative) rendering option A as correct. But what I don't get is the intuition behind it. I've always solved graphs intuitively without equations and stuff and my first guess was C because the acceleration must be like constant? for the velocity distance graph to turn out to be a straight line? It's kinda my guess that if acceleration itself varied with distance then velocity graph would be curved (basically intuition, no hard proof). But then C has slope $0$ which disagrees with my intuition. If I'm moving with a constant retardation, my velocity will keep on decreasing linearly innit? Please help me understand without involving maths. ($m=\frac{-v_0}{x_0}$ to be precise)

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    $\begingroup$ There must be more to this question than you present. Can you give us the text of the complete problem? Also, your expression for $a$ can't be correct if $m$ is the slope of some line. Advice: please don't post links to off-site locations. The targeted location might disappear. Especially in this case, as the image is stored in a Google drive. Are you prepared to guarantee that you will never delete or move the image? Broken links on this site do happen, and they render the question or answer useless. $\endgroup$ – garyp May 9 at 13:09
  • $\begingroup$ Rew, it would be a good idea for you to develop more trust in following mathematical solutions rather than depending on "intuition". In my experience, there are many physics problems where the math takes unusual and non-intuitive twists and turns before turning into an answer that can be associated with a physical phenomenon. $\endgroup$ – David White May 9 at 17:57
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The acceleration is not constant (it depends on x which changes with time). For a constant a, you would need v = vo + mt, (not mx).

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