Work Energy Power

JEE Main level, numerical answer, medium

159 of 183

Question 159 of 183

A body of mass 2kg2kg is driven by an engine delivering a constant power of 1Js−11J{s}^{-1}. the body starts from rest and moves in a straight line. After 9s9s, the body has moved a distance (in mm)….

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Answer: 18

Given,
Power delivered by the engine P=1Js−1P=1J{s}^{-1}
Mass of the body is m=2kgm=2kg
Body starts from the rest, u=0u=0
Using work energy Theorem,
W=∆K=PtW=∆K=Pt
Pt=12mv2−0Pt=\dfrac{1}{2}m{v}^{2}-0
Substitute the values in the above equation, we get
(1)t=12×2×v2(1)t=\dfrac{1}{2}\times 2\times {v}^{2}
⇒v=t=dsdt\Rightarrow v=\sqrt{t}=\dfrac{ds}{dt}
⇒∫0tds=∫09tdt\Rightarrow {\int }_{0}^{t}ds={\int }_{0}^{9}\sqrt{t}dt
⇒s=(9)3232=23×27\Rightarrow s=\dfrac{{\left(9\right)}^{\dfrac{3}{2}}}{\dfrac{3}{2}}=\dfrac{2}{3}\times 27
⇒s=18m\Rightarrow s=18m

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