An object is at rest at $(4 ,1 ,6 )$ and constantly accelerates at a rate of $4/3 m/s^2$ as it moves to point B. If point B is at $(3 ,5 ,7 )$ , 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 · 2016-04-08T17:06:29

$t=2,52 " s"$

$"the point of A:(4,1,6)"$
$"the point of B:(3,5,7)"$

$"distance between the point A and B :"$
$s=sqrt((A_x-B_x)^2+(A_y-B_y)^2+(A_z-B_z)^2)$

$s=sqrt((4-3)^2+(1-5)^2+(6-7)^2)$

$s=sqrt(1^2+(-4)^2+(-1)^2)$

$s=sqrt(1+16+1)=sqrt18$

$s=4,24" m"$

$"distance equation for an object starting from rest:"$

$s=1/2*a *t^2$

$"a:acceleration of object"$

$"t:elapsed time"$
$"given "a=4/3 m/s^2$

$4,24=1/2*4/3*t^2$

$t^2=(6*4,24)/4$

$t^2=6,36$

$t=2,52 " s"$

An object is at rest at (4 ,1 ,6 )(4 ,1 ,6 ) and constantly accelerates at a rate of 4/3 m/s^24/3 m/s^2 as it moves to point B. If point B is at (3 ,5 ,7 )(3 ,5 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.