An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <5 N , 6 N># and the second is #F_2 = < 1 N, -4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-12-27T16:16:09

The answer is #=3.16ms^(-2)# at #18.4º#

The net force is

#=vecF=vecF_1+vecF_2#

#vecF=〈1,-4〉+〈5,6〉=〈6,2〉#

The magnitude of #vecF=∥〈6,2〉∥=sqrt(36+4)=sqrt40#

As, #F=m*a#

#a=F/m=sqrt40/2=2sqrt10/20=sqrt10=3.16ms^(-2)#

The direction is

#tantheta=2/6=1/3#

#theta=18.4º#