An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :
Solution
P = const.<br><br>$P = Fv = {{m{v^2}dv} \over {dx}}$<br><br>$\int\limits_0^x {{P \over m}dx} = \int\limits_0^v {{v^2}dv}$<br><br>${{Px} \over m} = {{{v^3}} \over 3}$<br><br>${\left( {{{3Px} \over m}} \right)^{1/3}} = v = {{dx} \over {dt}}$<br><br>$${\left( {{{3P} \over m}} \right)^{1/3}}\int\limits_0^t {dt} = \int\limits_0^x {{x^{ - 1/3}}} dx$$<br><br>$\Rightarrow x = {\left( {{{8P} \over {9m}}} \right)^{1/2}}{t^{3/2}}$
About this question
Subject: Physics · Chapter: Work, Energy and Power · Topic: Work Done by a Force
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