First slide

Power

Question

A force F acting on a body depends on its displacement s as $F \propto s^{- 1 / 3}$ . The power delivered by F will depend on displacement as

Moderate

A

$s^{2 / 3}$
B

$s^{- 5 / 3}$
C

$s^{1 / 2}$
D

$s^{0}$

Solution

$F \propto s^{- 1 / 3} or a \propto s^{- 1 / 3}$
or $v d v \propto s^{- 1 / 3} d s$ $(∵ a = v \cdot \frac{d v}{d s})$
On integrating, we have
$v^{2} \propto s^{2 / 3}$ or $v \propto s^{V 3}$
Now, power, $P = F \cdot v \propto s^{- 1 / 3} \cdot s^{1 / 3} or ∣ P \propto s^{0}$

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