An object is at rest at #(2 ,9 ,5 )# and constantly accelerates at a rate of #1/5 m/s# as it moves to point B. If point B is at #(6 ,2 ,7 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Question
Answer 1

#t = 9.11# #"s"#

NOTE: I'll assume the given acceleration is #1/5# #"m/s"^2#, not #1/5# #"m/s"#.
We're asked to find the time #t# it takes an object to travel a certain distance with a given constant acceleration.
#Deltax = v_(0x)t + 1/2a_xt^2#
#Deltax = sqrt((6-2)^2 + (2-9)^2 + (7-5)^2) = 8.31# #"m"#
#v_(0x)# is the initial velocity, which is #0# since it started from rest
#t# is the time (we're trying to find this)
#a_x# is the constant acceleration (given as #1/5# #"m/s"^2#)
#8.31# #"m"# #=0t + 1/2(1/5color(white)(l)"m/s"^2)t^2#
#t = sqrt((8.31color(white)(l)"m")/(1/10color(white)(l)"m/s"^2)) = color(red)(ul(9.11color(white)(l)"s"#
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Answer 2
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