An object with a mass of #9 kg# is acted on by two forces. The first is #F_1= < -7 N , -1 N># and the second is #F_2 = < 4 N, -5 N>#. What is the objects rate and direction of acceleration?

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Answer 1 · 2017-03-11T14:25:30

The rate of acceleration is #=0.75ms^-2# in the direction #=243.4#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-7,-1>+<4,-5>#

#=<-3,-6>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/9<-3,-6> = <-1/3, -2/3>#

The magnitude of the acceleration is

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

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

#=sqrt(5)/3=0.75ms^-2#

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

The angle is in the 3rd quadrant

#theta=arctan(2)= 243.4#º