An object with a mass of #6 kg# is acted on by two forces. The first is #F_1= < -1 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 · 2017-02-21T14:12:40

The net acceleration is #=1.67ms^-2# in the direction #=53.1#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-1,5>+<7,3>#

#=<6,8>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/6<6,8> = <1, 4/3>#

The magnitude of the acceleration is

#||veca||=||<1,4/3>||#

#=sqrt((1)^2+(4/3)^2)#

#=sqrt(1+16/9)#

#=sqrt 25/3=1.67ms^-2#

The direction is #theta = arctan((4/3)/(1))#

The angle is in the 1st quadrant

#theta=arctan(4/3)=53.1#º