Answer to Question #135487 in Mechanical Engineering for Fredrick Moleleki

Question #135487
A particle moves in a straight line such that the velocity is 5 + 3cosX. Given that the displacement is zero when the time is zero , find an expression of time as a function of the displacement
1
Expert's answer
2020-09-30T10:21:16-0400

"v=5+3\\cdot\\cos x\\to \\frac{dx}{dt}=5+3\\cdot\\cos x\\to"


"dt=\\frac{1}{5+3\\cdot\\cos x}dx\\to"


"\\int dt=\\int \\frac{1}{5+3\\cdot\\cos x}dx" "\\to t=\\frac{tan^{-1}(\\frac{\\tan(x\/2)}{2})}{2}+C"


if "x=0" then "t=0\\to C=0"


So,


"t=\\frac{tan^{-1}(\\frac{\\tan(x\/2)}{2})}{2}" . Answer







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