An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <5 N , 7 N># and the second is #F_2 = < 2 N, -4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-11-01T17:55:14

The rate of acceleration is #=3.81ms^-2# in the direction #=23.2^@# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2=<5,7> + <2,-4> = <7,3>#

The mass is #m=2kg#

According to Newton's Second Law of motion

#vecF=mveca#

The acceleration is

#veca=1/mvecF=1/2 <7,3> = <7/2,3/2>#

The rate of acceleration is

#||veca|| =| |<7/2,3/2>|| = sqrt((7/2)^2+(3/2)^2)=sqrt(49/4+9/4)=sqrt58/2=3.81ms^-2#

The direction of acceleration is

#theta = arctan((3/2)/(7/2))=arctan(3/7)=23.2^@# anticlockwise from the x-axis.