An object is at rest at $(1 ,5 ,1 )$ and constantly accelerates at a rate of $4/3 m/s^2$ as it moves to point B. If point B is at $(9 ,4 ,8 )$ , 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 · 2016-04-16T22:01:56

$t~=4" s"$

$A=(1,5,1)" the point of A"$

$B=(9,4,8)" the point of B"$

$A_x=1" "A_y=5" "A_z=1$

$B_x=9" "B_y=4" "B_z=8$

$"let's calculate distance between the points A and B"$

$Delta s=sqrt((B_x-A_x)^2+(B_y-A_y)^2+(B_z-A_z)^2)$

$Delta s=sqrt((9-1)^2+(4-5)^2+(8-1)^2)$

$Delta s=sqrt(8^2+(-1)^2+7^2)$

$Delta s=sqrt(64+1+49)$

$Delta s=10,68" m"$

$a=4/3 m/s^2 "acceleration of object"$

$t="elapsed time from the point of A to the point of B"$

$Delta s=1/2 *a*t^2$
$"distance equation for an object moving from rest"$

$10,68=1/2*4/3*t^2$

$t^2=(3*10,68)/2$

$t^2=16,02$

$t~=4" s"$

An object is at rest at (1 ,5 ,1 )(1 ,5 ,1 ) 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 (9 ,4 ,8 )(9 ,4 ,8 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.