An object with a mass of #5 kg# is acted on by two forces. The first is #F_1= < 1 N , -1 N># and the second is #F_2 = < 5 N, 2 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-03-22T08:03:20

The rate of acceleration is #=1.2ms^-2# in the direction #=9.5#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <1,-1>+<5,2>#

#=<6,1>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/5<6,1> = <6/5, 1/5>#

The magnitude of the acceleration is

#||veca||=||<6/5,1/5>||#

#=sqrt((6/5)^2+(1/5)^2)#

#=sqrt(37)/5=1.22ms^-2#

The direction is #theta = arctan((1/5)/(6/5))#

The angle is in the 1st quadrant

#theta=arctan(1/6)= 9.5#º