An object is at rest at $(9 ,1 ,3 )$ and constantly accelerates at a rate of $1/4 m/s^2$ as it moves to point B. If point B is at $(6 ,8 ,2 )$ , 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 · 2017-08-11T06:18:10

The time is $=15.7s$

The distance $AB$ is

$AB=sqrt((6-9)^2+(8-1)^2+(2-3)^2)=sqrt((-3)^2+(7)^2+(-1)^2)$

$=sqrt(9+49+1)=sqrt59m$

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

The initial velocity is $u=0ms^-1$

We apply the equation of motion

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

So,

$sqrt59=0+1/2*(1/4)^2*t^2$

$t^2=32sqrt59$

$t=sqrt(32sqrt59)=15.7s$

An object is at rest at (9 ,1 ,3 )(9 ,1 ,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 ,8 ,2 )(6 ,8 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.