Work, Energy and Power

Question

A body is moving along a straight line by a machine delivering constant power. How does the distance travelled by body will depend upon time?

Solution

We have,

Power, $P equals F v$
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$rightwards double arrow$ $vdv equals straight P over straight m dt$
Integrating both sides, we have,
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$rightwards double arrow$ $straight v equals dx over dt equals square root of fraction numerator 2 straight P over denominator straight m end fraction end root left parenthesis straight t right parenthesis to the power of 1 divided by 2 end exponent$
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On integrating both sides, we have
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$rightwards double arrow$ $straight x equals square root of fraction numerator 2 straight P over denominator straight m end fraction end root space open parentheses 2 over 3 left parenthesis straight t right parenthesis to the power of 3 divided by 2 end exponent close parentheses$
$rightwards double arrow$ $straight x equals open parentheses square root of fraction numerator 8 straight P over denominator 9 straight m end fraction end root close parentheses straight t to the power of 3 divided by 2 end exponent$
∴ $straight x proportional to straight t to the power of 3 divided by 2 end exponent$
x is the distance and t is the time travelled.

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Work, Energy And Power

A body is moving along a straight line by a machine delivering constant power. How does the distance travelled by body will depend upon time?

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