An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < 2 N , 3 N># and the second is #F_2 = < -7 N, 1 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2018-04-23T11:58:10

The rate of acceleration is #=3.2ms^-1# in the direction #=141.3^@#anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF= <2,3> + <-7,1> = <2-7, 3+1> #

# = <-5,4> N#

The mass of the object is #m=2kg#

#vecF=mxx veca#

Therefore,

#veca=1/m*vecF= 1/2* <-5,4> #

#= <-5/2, 2> ms^-2#

The rate of acceleration is

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

#=sqrt(25/4+4)= sqrt41/2=3.20ms^-2#

The direction is

#theta=arctan((-4)/(5)) = 180^@-arctan(4/5)=141.3^@# anticlockwise from the x-axis