An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -7 N , 4 N># and the second is #F_2 = < 8 N, -2 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2018-01-19T06:48:53

The rate of acceleration is #=sqrt5/4 ms^-2# in the direction #=63.4^@# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#vecF_1= <-7,4>#

#vecF_2= <8, -2>#

#vecF=<-7,4> + <8, -2> =<1,2> N#

The mass is #m=4kg#

According to Newton's Second Law of motion

#vecF=mxxveca#

The acceleration is

#veca=1/mxxvecF=1/4 * <1,2> = <1/4, 1/2> ms^-2#

The rate of acceleration is

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

#=sqrt(1/16+1/4) = sqrt(5/16)#

#=sqrt5/4ms^-2#

The direction is

#theta=arctan(2/1)=63.4^@# anticlockwise from the x-axis