An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <5 N , 1 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 · 2017-08-12T15:56:24

#|vec a| ~~ 3.8 m*s^(-2)#

#hata = 1/sqrt(58)(7hati - 3hatj)#

#vec F_1 = (5hati + hatj) N#

#vec F_2 = (2hati - 4hatj)N#

#vec F_(n et) = (7hati - 3hatj)N#

#m = 2kg#

#vec a = vec F/m#

#vec a = (7/2hati - 3/2hatj) m*s^(-2)#

#|vec a| = sqrt((7/2)^2 + (3/2)^2)#

#rArr |vec a| = sqrt(58)/2#

#rArr |vec a| ~~ 3.80 m*s^(-2)#

#vec a = |vec a| * hat a#

#hat a = vec a/|vec a|#

#rArr hat a = (7/2hati - 3/2hatj)* 2/sqrt(58)#

#rArr hat a = 1/(sqrt(58))(7hati - 3hatj) #