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Physics - W.E.P. Question with Solution | TestHub

PhysicsW.E.P.PowerHard2 minQB

PhysicsHardsingle choice

An automobile of mass $m$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $P$ . The position is given as a function of time by:

Options:

Answer:

Solution:

$P = const$

$P = F_{V} = \frac{m v^{2} d v}{d x}$

$\int_{0}^{x} \frac{P}{m} dx = \int_{0}^{v} v^{2} dv$

$\frac{P x}{m} = \frac{v^{3}}{3}$

${(\frac{3 P x}{m})}^{\frac{1}{3}} = v = \frac{d x}{d t}$

${(\frac{3 P}{m})}^{\frac{1}{3}} \int_{0}^{t} d t = \int_{0}^{x} x^{- \frac{1}{3}} d x$

$\Rightarrow x = {(\frac{8 P}{9 m})}^{\frac{1}{2}} t^{\frac{3}{2}}$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Power

⏱ 2mℹ️ Source: QB

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