An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -2 N , 4 N># and the second is #F_2 = < 3 N, -8 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-07-24T16:20:43

The rate of acceleration is #=1.12ms^-2# in the direction is #=116.6^@# anticlockwise from the x-axis.

The resultant force is

#vecF=vecF_1+vecF_2#

#=<-1, 4> + <3, -8>#

#= <2,-4> #

The acceleration is

#veca=1/4*<2, -4> = <1/2, -1>#

The rate of acceleration is

#=||<1/2,-1>|| = sqrt(1/4+1)=sqrt5/2=1.12ms^-1#

The direction is #theta=arctan(-1/(1/2))=arctan(-2)=116.6^@# anticlockwise from the x-axis