Work Power and Energy 1 Question 8

9. 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

$(1984,2 M)$

(a) $t^{1 / 2}$

(b) $t^{3 / 4}$

(c) $t^{3 / 2}$

(d) $t^{2}$

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Answer:

Correct Answer: 9. (c)

Solution:

  1. $P=$ constant

$\therefore$ Work done in time $t$.

$$ W=P t $$

From work-energy theorem, net work done is change in kinetic energy. Therefore,

$$ \frac{1}{2} m v^{2}=P t \text { or } v \propto t^{1 / 2} $$

Integrating, we get $\quad s \propto t^{3 / 2}$



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