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

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Answer 1 · 2017-11-17T07:05:37

The rate of acceleration is #=1.05ms^-2# in the direction #=71.6^@# anticlockwise from the x-axis

The resultant force is

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

#vecF=m veca#

The mass is #m =3kg#

The acceleration is

#veca=vecF/m= 1/3 < 1,3> = < 1/3, 1>m s^-2#

The rate of acceleration is

#=||vec a|| = ||<1/3,1>#

#=sqrt((1/3)^2+1^2)=sqrt(1/9+1)=sqrt10/3=1.05ms^-2#

The direction is

#theta= arctan(1/(1/3))=arctan(3)=71.6^@# anticlockwise from the x-axis