An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < -6 N , 2 N># and the second is #F_2 = < 1 N, 3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-23T17:43:25

The net acceleration is #=3.54ms^-2# in the direction of #=(3/4pi)rad#

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-6,2>+<1,3>#

#=<-5,5>#

#vecF=m veca#

#veca =1/m*vecF#

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

The magnitude of the acceleration is

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

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

#=sqrt(25/4+25/4)#

#=sqrt 50/2=3.54ms^-2#

The direction is #theta = arctan((5/2)/(-5/2))#

The angle is in the 2nd quadrant

#theta=arctan(-1)=(3/4pi) rad#