The velocity (v) - distance (x) graph is show | vedclass

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(B) The equation of the $v$ vs $x$ graph is a straight line with a negative slope and a positive intercept on the $v$-axis:$v = C_1 - C_2 x$, where $C

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(B) The equation of the $v$ vs $x$ graph is a straight line with a negative slope and a positive intercept on the $v$-axis:$v = C_1 - C_2 x$, where $C_1$ and $C_2$ are positive constants.The acceleration $a$ is given by the relation:$a = v \frac{dv}{dx}$Substituting the expression for $v$ and its derivative $\frac{dv}{dx} = -C_2$:$a = (C_1 - C_2 x) 	imes (-C_2)$$a = C_2^2 x - C_1 C_2$This equation is of the form $a = mx + c$, where the slope $m = C_2^2$ (positive) and the intercept $c = -C_1 C_2$ (negative).Thus, the graph of $a$ versus $x$ is a straight line with a positive slope and a negative intercept on the $a$-axis, which corresponds to option $B$.

The velocity $(v)$ - distance $(x)$ graph is shown in the figure. Which graph represents the acceleration $(a)$ versus distance $(x)$ variation of this system?

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