An object with a mass of #5 kg# is acted on by two forces. The first is #F_1= <2 N , 6 N># and the second is #F_2 = <4 N, -3 N>#. What is the objects rate and direction of acceleration?

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Answer 1 · 2018-04-02T07:00:04

The rate of acceleration is #=1.34ms^-2# in the direction #=26.6^@# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF= <2,6> + <4,-3> = <2+4, 6-3> #

# = <6,3> N#

The mass of the object is #m=5kg#

According to Newto's Second Law

#vecF=mxx veca#

Therefore,

#veca=1/m*vecF= 1/5* <6,3> = <6/5, 3/5> ms^-2#

The rate of acceleration is

#||veca|| = || <6/5,3/5> || = sqrt ((6/5)^2+(3/5)^2) #

#=sqrt(36/25+9/25)= sqrt45/5=1.34ms^-2#

The direction is

#theta=arctan((3/5)/(6/5)) = arctan(0.5)=26.6^@# anticlockwise from the x-axis