The given graph shows the variation of veloci | vedclass

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Question

(a) Given line have positive intercept but negative slope. So its equation can be written as

$v = - mx + {v_0}$&hellip;..(i)      &n

Vedclass · Accepted Answer

Vedclass · Answer

(a) Given line have positive intercept but negative slope. So its equation can be written as

$v = - mx + {v_0}$&hellip;..(i)       [where $m = 	an 	heta = \frac{{{v_0}}}{{{x_0}}}$]

By differentiating with respect to time we get $\frac{{dv}}{{dt}} = - m\frac{{dx}}{{dt}} = - mv$

Now substituting the value of $v$ from eq. (i) we get $\frac{{dv}}{{dt}} = - m[ - mx + {v_0}] = {m^2}x - m{v_0}$

$	herefore a = {m^2}x - m{v_0}$

i.e. the graph between $a$ and $x$ should have positive slope but negative intercept on $a-$axis. So graph $(a) $ is correct.

Graph	Characteristics
$(A)$	$(i)$ has $v > 0$ and $a < 0$ throughout
$(B)$	$(ii)$ has $x > 0,$ throughout and has a point with $v = 0$ and a point with $a = 0$
$(C)$	$(iii)$ has a point with zero displacement for $t > 0$
$(D)$	$(iv)$ has $v < 0$ and $a > 0$

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement

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