An object is at rest at $(4 ,5 ,1 )$ and constantly accelerates at a rate of $4/3 m/s^2$ as it moves to point B. If point B is at $(7 ,9 ,6 )$ , 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 · 2018-05-03T06:55:49

The time is $=3.26s$

The distance $AB$ is

$AB=sqrt((7-4)^2+(9-5)^2+(6-1)^2)=sqrt(9+16+25)=sqrt(50)m$

Apply the equation of motion

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

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

The acceleration is $a=4/3ms^-2$

Therefore,

$sqrt50=0+1/2*4/3*t^2$

$t^2=3/2sqrt50$

$t=sqrt(3/2sqrt50)=3.26s$

An object is at rest at (4 ,5 ,1 )(4 ,5 ,1 ) and constantly accelerates at a rate of 4/3 m/s^24/3 m/s^2 as it moves to point B. If point B is at (7 ,9 ,6 )(7 ,9 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.