An object with a mass of #14# #kg# is acted on by two forces. The first is #F_1= < 5 N , 3 N># and the second is #F_2 = < 2 N, 7 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-05-22T00:02:48

The acceleration will be #0.87# #ms^-2# at #55^o# to the positive x-axis.

First find the magnitude of the force acting, which is the vector sum of the forces:

#F=sqrt((5+2)^2+(3+7)^2)==sqrt(7^2+10^2)=sqrt(49+100)#
#=sqrt(149)~~12.2# #N#

#a=F/m=12.2/14~~0.87# #ms^-2#

To find the direction:

#tan theta="opposite"/"adjacent"=10/7#

Which yields #theta=55^o#