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Question

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $$t$$ is proportional to:


A
t3/2
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B
t1/2
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C
t3/4
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D
t2
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Solution

The correct option is A $${ t }^{ 3/2 }$$
$$Power\quad =\dfrac { w }{ t } =\dfrac { \dfrac { 1 }{ 2 } mv^{ 2 } }{ t } =constant$$
$$\therefore $$   $${ v }^{ 2 }\propto t$$
$${ v }^{ 2 }\propto t$$    
$$ v \propto { t }^{ 1/2 }$$
$$\therefore $$ Displacement(magnitude)= Velocity x Time
                                              $$ =  v \times  t$$   $$\propto \ { t }^{ 1/2 }\times t={ t }^{ 3/2 }$$                                         

Physics

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