An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < 6 N , 4 N># and the second is #F_2 = < -3 N, -2 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-05-20T10:00:52

The rate of acceleration is #=0.9ms^-2# in the direction #=33.7º# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#= <6,4>+<-3,-2>#

#=<3,2>#

#vecF=m veca#

Mass, #m=4kg#

#veca =1/m*vecF#

#=1/4<3,2> = <3/4, 1/2>#

The magnitude of the acceleration is

#||veca||=||<3/4,1/2>||#

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

#=sqrt(0.8125)=0.9ms^-2#

The direction is #theta = arctan((1/2)/(3/4))#

The angle lies in the 1st quadrant

#theta=arctan(2/3)=33.7º# anticlockwise from the x-axis