An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 1 N , 4 N># and the second is #F_2 = < 2 N, -3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-08-06T23:25:12

Rate of acceleration
#abs (vec a) = sqrt(1^2 + (1/3)^2) = sqrt(10)/3 \ m/s^2#

Direction
#arctan (1/3)# measured CCW from x-axis

#Sigma vec F = m vec a#

here

#((1),(4)) + ((2),(-3)) = 3 ((a_x), (a_y))#

#((3),(1)) = 3 ((a_x), (a_y))#

#((a_x), (a_y)) = ((1),(1/3))#

Rate of acceleration
#abs (vec a) = sqrt(1^2 + (1/3)^2) = sqrt(10)/3 \ m/s^2#

direction is: #arctan (1/3)# measured CCW from x-axis