An object is at rest at $(4 ,8 ,2 )$ and constantly accelerates at a rate of $4/3 m/s^2$ as it moves to point B. If point B is at $(8 ,1 ,7 )$ , 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 · 2017-04-19T13:52:15

The time is $=3.77s$

The distance between the points $A=(x_A,y_A,z_A)$ and the point $B=(x_B,y_B,z_B)$ is

$AB=sqrt((x_B-x_A)^2+(y_B-y_A)^2+(z_B-z_A)^2)$

$d=AB= sqrt((8-4)^2+(1-8)^2+(7-2)^2)$

$=sqrt(4^2+(-7)^2+5^2)$

$=sqrt(16+49+25)$

$=sqrt90$

We apply the equation of motion

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

$u=0$

so,

$d=1/2at^2$

$t^2=(2d)/a=(2sqrt90)/(4/3)$

$=14.23$

$t=sqrt(14.23)=3.77s$

An object is at rest at (4 ,8 ,2 )(4 ,8 ,2 ) 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 (8 ,1 ,7 )(8 ,1 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.