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

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Answer 1 · 2018-04-19T14:51:26

The rate of acceleration is #=1.20ms^-2# in the direction #=213.7^@# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF= <-6,-5> + <3,3> = <-6+3, -5+3> #

# = <-3,-2> N#

The mass of the object is #m=3kg#

#vecF=mxx veca#

Therefore,

#veca=1/m*vecF= 1/3* <-3,-2> #

#= <-1, -2/3> ms^-2#

The rate of acceleration is

#||veca|| = || <-1,-2/3> || = sqrt ((-1)^2+(-2/3)^2) #

#=sqrt(1+4/9)= sqrt13/3=1.20ms^-2#

The direction is

#theta=arctan((-2/3)/(-1)) = 180^@+arctan(2/3)=213.7^@# anticlockwise from the x-axis