An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < -2 N , -5 N># and the second is #F_2 = < 7 N, 3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-08-19T23:26:33

rate : # sqrt 29/3 m "/" s^2#

direction : # arctan (-(2)/(5)) #

#Sigma vec F = m vec a#

Here

#Sigma vec F = ((-2),(-5)) + ((7),(3)) = ((5),(-2)) = color(red)(m vec a)#

#implies ((5),(-2)) = 3 ((a_x),(a_y))#

#implies vec a = 1/3((5),(-2)) #

#abs(vec a) = 1/3 sqrt(5^2 + (-2)^2) = sqrt 29/3#

#tan varphi = (-2)/(5) implies varphi = arctan (-(2)/(5)) #