An object with a mass of #6 kg# is acted on by two forces. The first is #F_1= < -6 N , 2 N># and the second is #F_2 = < 1 N, 3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-11-07T13:43:48

The rate of acceleration is #=1.18ms^-1# in the direction #=135^@# anticlockwise from the x-axis.

The resultant force is

#vecF=vecF_1+vecF_2=<-6,2> + <1,3> = <-5,5>#

The mass is #m=6kg#

According to Newton's Second Law of motion

#vecF=mveca#

The acceleration is

#veca=1/mvecF=1/6<-5,5> = <-5/6,5/6>#

The rate of acceleration is

#||veca|| =| |<-5/6,5/6>|| = sqrt((-5/6)^2+(5/6)^2)=sqrt(25/36+25/36)=sqrt50/6=1.18ms^-2#

The direction of acceleration is

#theta = arctan((5/6)/(-5/6))=arctan(-1)=135^@# antilockwise from the x-axis.