An object with a mass of #8 kg# is acted on by two forces. The first is #F_1= < -2 N , 1 N># and the second is #F_2 = < 3 N, -4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-27T13:01:33

The rate of acceleration is #=0.4ms^-2#
in the direction of #=288.4#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-2,1>+<3,-4>#

#=<1,-3>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/8<1,-3> = <1/8, -3/8>#

The magnitude of the acceleration is

#||veca||=||<1/8,-3/8>||#

#=sqrt((1/8)^2+(-3/8)^2)#

#=sqrt(1/64+9/64)#

#=sqrt 10/8=0.4ms^-2#

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

The angle is in the 4th quadrant

#theta=arctan(-3)= 288.4#º