A 3.00 kg object is moving in aplane, with its x and y coordinates given by x =

Question

A 3.00 kg object is moving in aplane, with its x and y coordinates given byx = 2t2 -4 and y = 3t3 + 5,where x and y are in meters and t is inseconds. Find the magnitude of the net force acting on this objectat t = 1.80 s
                           N   (units for final answer) A 3.00 kg object is moving in aplane, with its x and y coordinates given byx = 2t2 -4 and y = 3t3 + 5,where x and y are in meters and t is inseconds. Find the magnitude of the net force acting on this objectat t = 1.80 s
                           N   (units for final answer)

Explanation / Answer

mass m = 3 kg positon in x direction  x = 2t^2 -4 velocioty in x direction v = dx / dt =4 t accleration in x direction a = dv / dt                                         = 4 force in x direction F = ma = 3 * 4 = 12 N position in y direction y = 3t^3 + 5 velocity in y direction V = dy / dt = 9t ^ 2 accleration in y direction a ' = dV / dt = 18 t Accleration at t= 1.8 s is a ' = 18 * 1.8 = 32.4 m/ s ^ 2 force in y direction F ' = m a ' = 97.2 N magnitude of the net force acting on this object at t= 1.80 s is F " = [ F ^ 2 + F' ^ 2 ]                                                                                                    = 97.93 N

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