An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < -9 N , 8 N># and the second is #F_2 = < 4 N, -1 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-03-25T06:46:33

The rate of acceleration is #=4.3ms^-2# in the direction of #=125.5#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-9,8>+<4,-1>#

#=<-5,7>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/2<-5,7> = <-5/2, 7/2>#

The magnitude of the acceleration is

#||veca||=||<-5/2,7/2>||#

#=sqrt((-5/2)^2+(7/2)^2)#

#=sqrt(74)/2=4.3ms^-2#

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

The angle is in the 2nd quadrant

#theta=arctan(-7/5)=125.5 #º