An object is at rest at #(9 ,7 ,3 )# and constantly accelerates at a rate of #1/4 m/s^2# as it moves to point B. If point B is at #(6 ,8 ,2 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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Answer 1 · 2016-04-04T20:57:36

#t=25,53 s#

#"let's find distance between (9,7,3) and (6,8,2)"#

#Delta s=sqrt((6-9)^2+(8-7)^2+(2-3)^2)#
#Delta s=sqrt((-3)^2+1^2+(-1)^2)#

#Delta s=sqrt(9+1+1)" "Delta s=sqrt11" m"#

#"distance equation for an object starting from rest:"#

#Delta s=1/2*a t^2#

#a:"acceleration"#
#t:"time"#

#sqrt11=1/2*1/4*t^2#
#t^2=8 sqrt11#

#t^2=sqrt (64*11)#

#t^2=sqrt 704#

#t=25,53 s#