An object with a mass of #14 kg# is acted on by two forces. The first is #F_1= < 5 N , 6 N># and the second is #F_2 = < 3 N, 4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-03-03T10:55:07

The rate of acceleration is #=0.92ms^-2# in the direction #51.3º#

The resultant force is

#vecF=vecF_1+vecF_2#

#= <5,6>+<3,4>#

#=<8,10>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/14<8,10> = <4/7, 5/7>#

The magnitude of the acceleration is

#||veca||=||<4/7,5/7>||#

#=sqrt((4/7)^2+(5/7)^2)#

#=sqrt(16/49+25/49)#

#=sqrt 41/7=0.92ms^-2#

The direction is #theta = arctan((10)/(8))#

The angle is in the 1st quadrant

#theta=arctan(5/4)= 51.3#º