An object is at rest at $(1 ,2 ,9 )$ and constantly accelerates at a rate of $1 m/s^2$ as it moves to point B. If point B is at $(6 ,1 ,3 )$ , 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 · 2018-03-20T06:44:15

The time is $=4.0s$

The distance $AB$ is

$AB=sqrt((6-1)^2+(1-2)^2+(3-9)^2)=sqrt(25+1+36)=sqrt(62)m$

Apply the equation of motion

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

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

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

Therefore,

$sqrt62=0+1/2*1*t^2$

$t^2=2*sqrt62$

$t=sqrt(2*sqrt62)=4.0s$

An object is at rest at (1 ,2 ,9 )(1 ,2 ,9 ) and constantly accelerates at a rate of 1 m/s^21 m/s^2 as it moves to point B. If point B is at (6 ,1 ,3 )(6 ,1 ,3 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.