An object is at rest at $(4 ,8 ,3 )$ and constantly accelerates at a rate of $4/3 m/s^2$ as it moves to point B. If point B is at $(3 ,5 ,7 )$ , 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 · 2018-01-31T10:43:51

The time is $=2.77s$

The distance $AB$ is

$AB=sqrt((3-4)^2+(5-8)^2+(7-3)^2)=sqrt(1+9+16)=sqrt(26)m$

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,

$sqrt26=0+1/2*4/3*t^2$

$t^2=3/2*sqrt26$

$t=sqrt(3/2*sqrt26)=2.77s$

An object is at rest at (4 ,8 ,3 )(4 ,8 ,3 ) 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 (3 ,5 ,7 )(3 ,5 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.