An object is at rest at #(8 ,4 ,2 )# and constantly accelerates at a rate of #4/3 m/s# as it moves to point B. If point B is at #(3 ,1 ,6 )#, 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 · 2017-03-06T05:16:13

#sqrt(21/2)s#

let initial point A be (8,4,2) and final point B be (3,1,6)

by distance formula,

= #sqrt[(8-3)^2 + (4-1)^2 + (2-6)^2]#

#therefore# distance 's' between A and B is #sqrt50#

So, s = #sqrt50# = #5sqrt2# = #5*1.41# = 7m approx

also,
as object is at rest and starts constantly accelerating,
initial velocity ' u' = 0

By using equation,
s = ut + #1/2at^2#

as u = 0, s = #1/2at^2#

7 = #1/2*4/3t^2#

t = #sqrt(21/2)#s