An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -3 N , 6 N># and the second is #F_2 = < 7 N, -8 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-08-13T09:45:14

#theta = arctan (-1/2)#

#abs (vec a) = sqrt 5 / 2 "m/"s^2#

#Sigma vec F = m vec a#

#implies ((-3),(6))+ ((7),(-8)) = 4 ((a_x),(a_y))#

#((4),(-2))= 4 ((a_x),(a_y))#

# ((a_x),(a_y)) = ((1),(-1/2)) #

direction #tan theta = (a_y)/(a_x) = (-1/2)/(1)#, #theta = arctan (-1/2)#

#abs (vec a) = sqrt (1^2 + (-1/2)^2) = sqrt 5 /2 "m/"s^2#