An object is at rest at $(2 ,9 ,8 )$ and constantly accelerates at a rate of $1/5 m/s$ as it moves to point B. If point B is at $(6 ,2 ,2 )$ , 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 · 2017-04-08T13:09:04

The time is $=10.02s$

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

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

$d=AB= sqrt((6-2)^2+(2-9)^2+(2-8)^2)$

$=sqrt(4^2+7^2+6^2)$

$=sqrt(16+49+36)$

$=sqrt101$

We apply the equation of motion

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

$u=0$

so,

$d=1/2at^2$

$t^2=(2d)/a=(2sqrt101)/(1/5)$

$=100.5$

$t=sqrt(100.5)=10.02s$

An object is at rest at (2 ,9 ,8 )(2 ,9 ,8 ) and constantly accelerates at a rate of 1/5 m/s1/5 m/s as it moves to point B. If point B is at (6 ,2 ,2 )(6 ,2 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.