An object is at rest at $(2 ,4 ,1 )$ and constantly accelerates at a rate of $4/5$ $ms^-1$ as it moves to point B. If point B is at $(6 ,6 ,7 )$ , 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 · 2016-05-07T09:39:54

The distance between the points is $7.48$ $m$ .

The time taken is $t=sqrt(d/a)=sqrt(7.48/0.8)~~3.06$ $s$ .

First find the distance between the points:

$l=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$
$=sqrt((6-2)^2+(6-4)^2+(7-1)^2)=sqrt(16+4+36)$
$=sqrt56~~7.48$ $m$

An acceleration of $4/5$ can be expressed as $0.8$ .

$d=ut+at^2$ can be rearranged to $t=sqrt(d/a)$ when $u=0$ (which it is in this case).

An object is at rest at (2 ,4 ,1 )(2 ,4 ,1 ) and constantly accelerates at a rate of 4/54/5 ms^-1 ms^-1 as it moves to point B. If point B is at (6 ,6 ,7 )(6 ,6 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.