JEE MAIN - Physics (2017 - 8th April Morning Slot - No. 21)
Which graph corresponds to an object moving with a constant negative
acceleration and a positive velocity ?
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_8th_April_Morning_Slot_en_21_2.png)
_8th_April_Morning_Slot_en_21_3.png)
_8th_April_Morning_Slot_en_21_4.png)
Explanation
Given that,
acceleration (a) = $$-$$ C (constant)
$$\therefore\,\,\,$$ $${{dv} \over {dt}}$$ = $$-$$ c
$$ \Rightarrow $$$$\,\,\,$$ $${{dv} \over {dx}}$$ . $${{dx} \over {dt}}$$ = $$-$$ c
$$ \Rightarrow $$$$\,\,\,$$ $$\upsilon $$ $${{dv} \over {dx}}$$ = $$-$$ c
$$ \Rightarrow $$$$\,\,\,$$ $$\int {v\,dv} $$ = $$-$$ c$$\int {dx} $$
$$ \Rightarrow $$$$\,\,\,$$ $${{{v^2}} \over 2}$$ = $$-$$ cx + k
$$ \Rightarrow $$$$\,\,\,$$ x = $$-$$ $${{{v^2}} \over {2c}}$$ + $${k \over c}$$
From this equation we can say option (c) is the correct graph.
acceleration (a) = $$-$$ C (constant)
$$\therefore\,\,\,$$ $${{dv} \over {dt}}$$ = $$-$$ c
$$ \Rightarrow $$$$\,\,\,$$ $${{dv} \over {dx}}$$ . $${{dx} \over {dt}}$$ = $$-$$ c
$$ \Rightarrow $$$$\,\,\,$$ $$\upsilon $$ $${{dv} \over {dx}}$$ = $$-$$ c
$$ \Rightarrow $$$$\,\,\,$$ $$\int {v\,dv} $$ = $$-$$ c$$\int {dx} $$
$$ \Rightarrow $$$$\,\,\,$$ $${{{v^2}} \over 2}$$ = $$-$$ cx + k
$$ \Rightarrow $$$$\,\,\,$$ x = $$-$$ $${{{v^2}} \over {2c}}$$ + $${k \over c}$$
From this equation we can say option (c) is the correct graph.
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