An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <4 N , 6 N># and the second is #F_2 = < 1 N, -4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-11-16T06:20:22

The rate of acceleration is #=2.69ms^-1# in the direction #21.8^@# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2 = < 4, 6 > + <1, -4 > = < 5, 2> #

#vecF=m veca#

The mass is #m =2kg#

The acceleration is

#veca=vecF/m= 1/2 < 5,2> = < 5/2, 1>m s^-2#

The rate of acceleration is

#=||vec a|| = ||<5/2,1>#

#=sqrt((5/2)^2+1^2)=sqrt(25/4+1)=sqrt29/2=2.69ms^-2#

The direction is

#theta= arctan(2/5)=arctan(0.4)=21.8^@# anticlockwise from the x-axis