An object is at rest at $(2 ,8 ,6 )$ and constantly accelerates at a rate of $5/3 m/s^2$ as it moves to point B. If point B is at $(3 ,2 ,7 )$ , 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 · 2017-08-15T17:36:51

The time is $=2.11s$

The distance $AB$ is

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

$=sqrt(1+36+1)=sqrt38m$

The acceleration is $a=5/3ms^-2$

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

We apply the equation of motion

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

So,

$sqrt38=0+1/2*(5/3)^2*t^2$

$t^2=18/25sqrt38$

$t=sqrt(18/25sqrt38)=2.11s$

An object is at rest at (2 ,8 ,6 )(2 ,8 ,6 ) and constantly accelerates at a rate of 5/3 m/s^25/3 m/s^2 as it moves to point B. If point B is at (3 ,2 ,7 )(3 ,2 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.