InterviewSolution
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InterviewSolution
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derivations of equations of motion |
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Answer» v=u+at (1) First equation of Motion:V = u + atsoln.Consider a body of mass “m” having initial velocity “u”.Let after time “t” its final velocity becomes “v” due to uniform acceleration “a”.Now we know that:Acceleration = change in velocity/Time taken=> Acceleration = Final velocity-Initial velocity / time taken=> a = v-u /t=>at = v-uor v = u + atThis is the first equation of motion.—————————————-(2) Second equation of motion:s = ut + 1/2 at^2sol.Let the distance travelled by the body be “s”.We know thatDistance = Average velocity X TimeAlso, Average velocity = (u+v)/2.: Distance (t) = (u+v)/2 X t …….eq.(1)Again we know that:v = u + atsubstituting this value of “v” in eq.(2), we gets = (u+u+at)/2 x t=>s = (2u+at)/2 X t=>s = (2ut+at^2)/2=>s = 2ut/2 + at^2/2or s = ut +1/2 at^2This is the 2nd equation of motion.……………………………………………………………(3) Third equation of Motionv^2 = u^2 +2assol.We know thatV = u + at=> v-u = ator t = (v-u)/a ………..eq.(3)Also we know thatDistance = average velocity X Time.: s = [(v+u)/2] X [(v-u)/a]=> s = (v^2 – u^2)/2a=>2as = v^2 – u^2or v^2 = u^2 + 2asThis is the third equation of motion.\xa0 v=u+at |
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