An object is at rest at $(2 ,1 ,4 )$ and constantly accelerates at a rate of $1/4 m/s^2$ as it moves to point B. If point B is at $(7 ,4 ,5 )$ , 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 · 2018-02-20T07:37:13

The time is $=6.88s$

The distance $AB$ is

$AB=sqrt((7-2)^2+(4-1)^2+(5-4)^2)=sqrt(25+9+1)=sqrt(35)m$

Apply the equation of motion

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

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

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

Therefore,

$sqrt35=0+1/2*1/4*t^2$

$t^2=8*sqrt35$

$t=sqrt(8*sqrt35)=6.88s$

An object is at rest at (2 ,1 ,4 )(2 ,1 ,4 ) 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 (7 ,4 ,5 )(7 ,4 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.