An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -1 N , 3 N># and the second is #F_2 = < 6 N, 5 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-06-03T18:27:56

The rate of acceleration is #=2.36ms^-2# in the direction of #=58º# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-1,3>+<6,5>#

#=<5,8>#

#vecF=m veca#

Mass, #m=4kg#

#veca =1/m*vecF#

#=1/4<5,8> = <5/4, 2>#

The magnitude of the acceleration is

#||veca||=||<5/4,2>||#

#=sqrt((5/4)^2+(2)^2)#

#=sqrt(5.5625)=2.36ms^-2#

The direction is #theta = arctan((8)/(5))#

The angle lies in the 1st quadrant

#theta=arctan(8/5)=58º# anticlockwise from the x-axis