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

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Answer 1 · 2017-01-13T17:01:03

The acceleration is #=〈-1/2,-3/2〉ms^-2# in the direction #251.6#º

The resultant force acting on the object is

#vecF=vecF_1+vecF_2#

#vecF=〈-4,2〉+〈2,-8〉=〈-2,-6〉#

By Newton`s secod Law

#vecF=m*veca#

#veca=vecF/m=1/4*〈-2,-6〉=〈-2/4,-6/4〉#

#veca=〈-1/2,-3/2〉#

The acceleration is #=〈-1/2,-3/2〉ms^-2#

The direction is #=180º+arctan((-3/2)/(-1/2))#

#=180º+arctan3=180+71.6=251.6#º