An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < -9 N , 8 N># and the second is #F_2 = < -7 N, -4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-11-14T06:45:24

The rate of acceleration is #=8.25ms^-2# in the direction is #=104^@# clockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2 = < -9, 8 > + <-7, -4 > = < -16, 4> #

#vecF=m veca#

The mass is #m =2kg#

The acceleration is

#veca=vecF/m= 1/2 < -16,4> = < -8, 2>m s^-2#

The rate of acceleration is

#=||vec a|| = ||<-8,2 >#

#=sqrt((-8)^2+2^2)=sqrt(64+4)=sqrt68=8.25ms^-2#

The direction is

#theta= arctan(-8/2)=arctan(-4)=180-76=104^@# clockwise from the x-axis