Question

Convert the shown $v-x$ graph to $a-x$ graph.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given curve is
So, we can write the equation from the graph as
$v=-\frac{v_0}{x_0}x+v_0$
Thus, we have
$a=\frac{dv}{dt}=\frac{d(-\frac{v_0}{x_0}x+v_0)}{dt}=-\frac{v_0}{x_0}\frac{dx}{dt}$
$\Rightarrow a=-\frac{v_0}{x_0}v=-\frac{v_0}{x_0}(-\frac{v_0}{x_0}x+v_0)$
$\Rightarrow a=-\frac{v_0^2}{x_0}(1-\frac{x}{x_0})=\frac{v_0^2}{x_0^2}x-\frac{v_0^2}{x_0}$
Hence, from the above equation we can see that the equation has slope positive and negative intercept value, so the possible $a-x$ graph is