An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < 8 N , 3 N># and the second is #F_2 = < -7 N, 1 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-12-28T08:08:33

The acceleration is #=2.06 ms^(-2)# at an angle of #76#º

The net force acting on the object is

#vecF=vecF_1+vecF_2#

#vecF=〈8,3〉+〈-7,1〉=〈1,4〉#

The magnitude of the force is #∥vecF∥=∥〈1,4〉∥#

#=sqrt(1+16)=sqrt17#

The acceleration is #=(∥vecF∥)/m=sqrt17/2=2.06 ms^(-2)#

The direction is #arctan(4/1)=76#º