An object is at rest at $(8 ,7 ,3 )$ and constantly accelerates at a rate of $1/4 m/s^2$ as it moves to point B. If point B is at $(6 ,3 ,4 )$ , 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 · 2018-07-10T05:21:10

The time is $=6.05s$

The distance $AB$ is

$d_(AB)=sqrt((6-8)^2+(3-7)^2+(4-3)^2)$

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

$=sqrt(4+16+1)$

$=sqrt(21)m$

The acceleration is $a=1/4ms^-2$

The initial velocity $u=0$

Apply the equation of motion

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

$sqrt(21)=0+1/2*1/4*t^2$

$t^2=8sqrt(21)$

$t=sqrt(8sqrt(21))=6.05s$

The time is $=6.05s$

An object is at rest at (8 ,7 ,3 )(8 ,7 ,3 ) and constantly accelerates at a rate of 1/4 m/s^21/4 m/s^2 as it moves to point B. If point B is at (6 ,3 ,4 )(6 ,3 ,4 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.