An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -5 N , 2 N># and the second is #F_2 = < -2 N, 3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-01-04T06:24:57

The acceleration is #=2.15ms^(-2)# at #144.5#º

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF=〈-5,2〉+〈-2,3〉=〈-7,5〉#

The magnitude of #vecF#, is #=∥vecF∥=∥〈-7,5〉∥#

#=sqrt(49+25)=sqrt74#

The rate of acceleration is #=(∥vecF∥)/m=sqrt74/4=2.15ms^(-2)#

The direction is #=arctan(-5/7)=144.5#º