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

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Answer 1 · 2018-05-04T06:10:37

The rate of acceleration is #=0.79ms^-1# in the direction #=18.4^@#clockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

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

# = <3,-1> N#

The mass of the object is #m=4kg#

#vecF=mxx veca#

Therefore,

#veca=1/m*vecF= 1/4* <3,-1> #

#= <3/4, -1/4> ms^-2#

The rate of acceleration is

#||veca|| = || <3/4,-1/4> || = sqrt ((3/4)^2+(-1/4)^2) #

#=sqrt(9/16+1/16)= sqrt10/4=0.79ms^-2#

The direction is

#theta=arctan((-1)/(3)) =18.4^@# clockwise from the x-axis