An object with a mass of #14 kg# is acted on by two forces. The first is #F_1= < 2 N , 7 N># and the second is #F_2 = < -9 N, 4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-20T10:51:37

The rate of acceleration is #=0.93ms^-2# in the direction #57.5#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <2,7>+<-9,4>#

#=<-7,11>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/14<-7,11> = <-1/2, 11/14>#

The magnitude of the acceleration is

#||veca||=||<-1/2,11/14>||#

#=sqrt((1/2)^2+(11/14)^2)#

#=sqrt(1/4+121/196)#

#=sqrt 0.867=0.93ms^-2#

The direction is #theta = arctan((11/14)/(1/2))#

The angle is in the 1st quadrant

#theta=arctan(11/7)=57.5#º