An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < -6 N , -5 N># and the second is #F_2 = < 7 N, 3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-07T06:49:52

The acceleration is #=0.75ms^-2# in the direction #=116.6#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-6,-5>+<7,3>#

#=<1,-2>#

#vecF=m veca#

#veca =1/m*vecF#

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

The magnitude of the acceleration is

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

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

#=sqrt(1/9+4/9)#

#=sqrt5/3=0.75ms^-2#

The direction is

#tantheta=(-2/3)/(1/3)=-2#

#theta=arctan(-2)=116.6#º