An object with a mass of #5 kg# is acted on by two forces. The first is #F_1= < 1 N , 4 N># and the second is #F_2 = < 2 N, -3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-06-28T08:24:55

#a=sqrt10/5" "m/s^2#

#"direction is shown in figure above."#

enter image source here

#"given:"#

#F_1= <1,4>" ; "vec F_1=i+4j#

#F_2= <2,-3>" ; "vec F_2=2i-3j#

#"first let's find the resultant force :"#

#F_R=(1+2)i+(4-3)j" ; "F_R=3i+j#

#"now let's find the magnitude of resultant force :"#

#F_"net"=sqrt(3^2+1^2)=sqrt(9+1)=sqrt10" "N#

#"And let's find acceleration using the newton's second law" #

#a=F_"net"/m#

#a:"represents acceleration of object"#
#m:"represents mass of object"#
#F_"net:""represents net force acting on object"#

#a=sqrt10/5" "m/s^2#

#"direction is shown in figure above."#