An object with a mass of #5 kg# is acted on by two forces. The first is #F_1= <10 N , 6 N># and the second is #F_2 = <4 N, 16 N>#. What is the objects rate and direction of acceleration?

1 Answer
Feb 17, 2018

The rate of acceleration is #=5.21ms^-2# in the derection #=57.5^@ "in the direction anticlockwise from the x- axis"#

Explanation:

The resultant force is

#vecF=vecF_1+vecF_2#

#= <10,6> + <4,16>#

#= <14, 22>N#

The mass of the object is #m=5kg#

According to Newton's Second Law

#vecF=mveca#

Therefore,

The acceleration is

#veca=vecF/m=1/5 *<14, 22>= <14/5, 22/5>#

The rate of acceleration is

#||veca||= ||<14/5, 22/5>||#

#=sqrt((14/5)^2+(22/5)^2)#

#=5.21ms^-2#

The direction is

#theta=arctan(22/14)=57.5^@ "in the direction anticlockwise from the x- axis"#