An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -2 N , -6 N># and the second is #F_2 = < 5 N, 3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-04T14:40:36

The acceleration is #=1.061ms^_2#
The direction is #-45#º

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF=<-2,-6>+<5,3>=<3,-3>#

#vecF=mveca#

#veca=1/mvecF#

#=1/4*<3,-3>=<3/4,-3/4>#

The magnitude of the acceleration is

#=sqrt((3/4)^2+(-3/4)^2)#

#=3/4sqrt(2)=1.061ms^-2#

The direction is

#tantheta=-(3/4)/(3/4)=-1#

#theta=-45#º