An object with a mass of #8 kg# is acted on by two forces. The first is #F_1= < -9 N , 7 N># and the second is #F_2 = < -4 N, -1 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-12-25T14:42:57

The answer is #=1.79ms^(-2)# at #155.2º#

The resultant force is
#vecF=vecF_1+vecF_2#

#vecF=〈-9,7〉+〈-4,-1〉=〈-13,6〉#

The magnitude of #vecF# is

#=∥〈-13,6〉∥#

#=sqrt(169+36)=sqrt205#

The acceleration is #=F/m=sqrt205/8=1.79ms^(-2)#

The direction of acceleration is #=arctan(-6/13)#

#=155.2º#