An object is at rest at $(1 ,2 ,1 )$ and constantly accelerates at a rate of $1/3$ $ms^-2$ as it moves to point B. If point B is at $(4 ,4 ,5 )$ , 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 · 2018-01-11T20:17:29

The distance between the two points is $5.4$ $m$ and the time taken to move from one to the other is $5.7$ $s$ .

First step is to find the distance between the two points:

$s=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$
$=sqrt((4-1)^2+(4-2)^2+(5-1)^2)=sqrt(3^2+2^2+4^2)$
$=sqrt(9+4+16)=sqrt(29)=5.4$ $m$

Now we know:

$u=0$ $ms^-1$ (since the object was initially at rest)
$a=1/3$ $ms^-2$
$s=5.4$ $m$ (some people use $d$ for distance)
$t=?$ $s$

We have the equation of motion:

$s=ut+1/2at^2$

The $ut$ term goes to 0 because $u=0$ , which makes life simpler:

$s=1/2at^2$

Rearranging to make $t$ the subject:

$t=sqrt((2s)/a)=sqrt((2xx5.4)/(1/3))=sqrt 32.4=5.7$ $s$

An object is at rest at (1 ,2 ,1 )(1 ,2 ,1 ) and constantly accelerates at a rate of 1/31/3 ms^-2ms^-2 as it moves to point B. If point B is at (4 ,4 ,5 )(4 ,4 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.