An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < 3 N , -4 N># and the second is #F_2 = < 7 N, 6 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-12-25T14:52:26

The answer is #=2.55ms^(-2)# at #11.31º#

The resultant force is
#vecF=vecF_1+vecF_2#

#vecF=〈3,-4〉+〈7,6〉=〈10,2〉#

The magnitude of #vecF# is

#=∥〈10,2〉∥#

#=sqrt(100+4)=sqrt104#

The acceleration is #=F/m=sqrt104/4=2.55ms^(-2)#

The direction of acceleration is #=arctan(2/10)#

#=11.31º#