An object with a mass of #14 kg# is acted on by two forces. The first is #F_1= < 4 N , 6 N># and the second is #F_2 = < 5 N, 9 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-04-04T06:52:34

The rate of acceleration is #=1.25ms^-2# in the direction #=59#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <4,6>+<5,9>#

#=<9,15>#

#vecF=m veca#

Mass, #m=14kg#

#veca =1/m*vecF#

#=1/14<9,15> = <9/14, 15/14>#

The magnitude of the acceleration is

#||veca||=||<9/14,15/14>||#

#=sqrt((9/14)^2+(15/14)^2)#

#=sqrt(306)/14=1.25ms^-2#

The direction is #theta = arctan((15)/(9))#

The angle is in the 1st quadrant

#theta=arctan(5/3)=59#º