એક કાર સ્થિર સ્થિતિમાંથી ગતિ શરૂ કરીને પ્રથમ | vedclass

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Question

(c) Let car starts from point $A$ from rest and moves up to point $B$ with acceleration $f$

Velocity of car at point $B$, $v = \sqrt {2fS} $

$As

Vedclass · Accepted Answer

$S = \frac{1}{{72}}f{t^2}$

Vedclass · Answer

(c) Let car starts from point $A$ from rest and moves up to point $B$ with acceleration $f$

Velocity of car at point $B$, $v = \sqrt {2fS} $

$As \,{v^2} = {u^2} + 2as]$

Car moves distance $BC$ with this constant velocity in time $t$

$x = \sqrt {2fS} \,.\,t$ ......(i) [As $s = ut$]

So the velocity of car at point $C$ also will be $\sqrt {2fs} $ and finally car stops after covering distance y.

Distance $CD &rArr;y = \frac{{{{(\sqrt {2fS} )}^2}}}{{2(f/2)}}$$ = \frac{{2fS}}{f} = 2S$....(ii) $[{\rm{As }}{v^{\rm{2}}} = {u^2} - 2as\, \Rightarrow \,s = {u^2}/2a]$

So, the total distance $AD$ = $AB + BC + CD=15S$ (given)

$&rArr;$ $S + x + 2S = 15S$ $&rArr; x = 12S$

Substituting the value of x in equation (i) we get

$x = \sqrt {2fS} \,.\,t &rArr; 12S = \sqrt {2fS} .t &rArr; 144{S^2} = 2fS.{t^2}$

$&rArr;$  $S = \frac{1}{{72}}f{t^2}$.

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જો ગતિમાન પદાર્થનો પ્રવેગ ધન હોય, તો $x \to t$ નો આલેખ દોરો.