An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < 3 N , 2 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 · 2016-12-21T06:54:27

The answer is #=3.2ms^(-2)# at #38.7º#

The resulting force is

#vecF=vecF_1+vecF_2#

#vecF=〈3,2〉+〈7,6〉=〈10,8〉#

The magnitude of #vecF# is

#=∥vecF∥ =∥〈10,8〉∥=sqrt(100+64)=sqrt164N#

The rate of acceleration is #=(∥vecF∥ )/m#

#=sqrt164/4=sqrt41/2=3.2ms^(-2)#

The direction is #=arctan(8/10)=38.7º#