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:

$t ~~ 7 s$

An object is at rest at (5 ,1 ,1 )(5 ,1 ,1 ) and constantly accelerates at a rate of 2/5 m/s2/5 m/s as it moves to point B. If point B is at (6 ,9 ,7 )(6 ,9 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.