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, 7 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-12-19T16:11:02

The answer is #=6.96ms^(-2)# and the direction is #69º#

The combination of the 2 forces is

#vecF=vecF_1+vecF_2#

#vecF=〈4,6〉+〈1,7〉=〈5,13〉#

The magnitude of #vecF# is

#∥vecF∥=∥〈5,13〉∥=sqrt(25+169)=sqrt194#

The rate of acceleration is #=(∥vecF∥)/m=sqrt194/2=6.96ms^(-2)#

The direction of acceleration is

#=arctan(13/5)=69º#