An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <5 N , 7 N># and the second is #F_2 = < 2 N, -2 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-08-10T23:21:45

#a = 1/2 sqrt 74# m/#s^2#
#theta_a = tan^(-1)( (5)/(7))#

#Sigma vec F = m vec a#

#Sigma vec F = ((5),(7)) + ((2),(-2)) = ((7),(5))#

#vec a = 1/m Sigma vec F = 1/2 ((7),(5))#

therefore :-)

#a = abs ( vec a) = 1/2 abs( ((7),(5))) = 1/2 sqrt 74#

#vec a#'s direction expressed as an angle #theta#, which is measured from the x axis, is:

#theta_a = tan^(-1)( (5)/(7))#