SATHEE: Work Energy And Power Question 260

Work Energy And Power Question 260

Question: A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ‘f’ is proportional to

Options:

A) $t^{3 / 4}$

B) $t^{3 / 2}$

C) $t^{1 / 4}$

D) $t^{1 / 2}$

Show Answer

Answer:

Correct Answer: B

Solution:

[b] We know that $F \times v = P o w e r$

$∴ F \times v = c$ where c = constant $a ∴ m \frac{d v}{d t} \times v = c (∴ F = m a = \frac{m d v}{d t})$

$∴ m \int_{0}^{v} v d v = c \int_{0}^{t} d t ∴ \frac{1}{2} m v^{2} = c t$

$∴ v = \sqrt{\frac{2 c}{m}} \times t^{^{1} /_{2}}$

$∴ \frac{d x}{d t} = \sqrt{\frac{2 c}{m}} \times t^{^{1} /_{2}} w h e r e v = \frac{d x}{d t}$

$∴ \int_{0}^{x} d x = \sqrt{\frac{2 c}{m}} \times \int_{0}^{t} t^{^{1} /_{2}} d t$

$x = \sqrt{\frac{2 c}{m}} \times \frac{2 t^{^{3} /_{2}}}{3} \Rightarrow x \propto t^{^{3} /_{2}}$

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Work Energy And Power Question 260

Question: A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ‘f’ is proportional to

Options:

Answer:

Solution:

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