An object is at rest at #(5 ,1 ,1 )# and constantly accelerates at a rate of #2/5 m/s# as it moves to point B. If point B is at #(6 ,9 ,7 )#, 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 · 2016-11-05T16:17:29

#t ~~ 7 s#

I am going to assume that there is a small typographical error in the units of the acceleration and it is #2/5m/s^2#

The distance, d, from Point #A = (5,1,1)# to point #B = (6,9,7)# is

#d =sqrt((6 -5)^2 + (9 - 1)^2 + (7 - 1)^2)#

#d =sqrt((1)^2 + (8)^2 + (6)^2)#

#d =sqrt(1 + 64 + 36)#

#d =sqrt(101) m#

The equation for distance traveled under constant acceleration is:

#d = (1/2)at^2#

Substitute #sqrt(101) m# for d and #2/5m/s^2# for a, and then solve for t:

#sqrt(101) m = (1/2)(2/5m/s^2)t^2#

#5sqrt(101)s^2 = t^2#

#t ~~ +-7 s#

But negative time does not make sense, therefore, make it only positive:

#t ~~ 7 s#