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.

Question

1220 views around the world

You can reuse this answer
Creative Commons License

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#