An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < 8 N , -5 N># and the second is #F_2 = < 6 N, 7 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-04-16T13:49:34

The rate of acceleration is #=7.07ms^-1# i the direction of #=8.13#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <8,-5>+<6,7>#

#=<14,2>#

#vecF=m veca#

Mass, #m=2kg#

#veca =1/m*vecF#

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

The magnitude of the acceleration is

#||veca||=||<7,1>||#

#=sqrt((7)^2+(1)^2)#

#=sqrt(50)=7.07ms^-2#

The direction is #theta = arctan((1)/(7))#

The angle is in the 1st quadrant

#theta=arctan(1/7)=8.13#º