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

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Answer 1 · 2017-03-27T12:41:43

The rate of acceleration is #=1.20ms^-2# in the direction of #=213.7#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-2,-3>+<-1,1>#

#=<-3,-2>#

#vecF=m veca#

Mass, #m=3kg#

#veca =1/m*vecF#

#=1/3<-3,-2> = <-1, -2/3>#

The magnitude of the acceleration is

#||veca||=||<-1,-2/3>||#

#=sqrt((-1)^2+(-2/3)^2)#

#=sqrt(13)/3=1.20ms^-2#

The direction is #theta = arctan((-2/3)/(-1))#

The angle is in the 3rd quadrant

#theta=arctan(2/3)=180+33.7=213.7#º