An object is at rest at $(1 ,9 ,2 )$ and constantly accelerates at a rate of $1/3 m/s$ as it moves to point B. If point B is at $(4 ,4 ,6 )$ , 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 · 2017-04-29T05:51:57

The time is $=6.51s$

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

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

$d=AB= sqrt((4-1)^2+(4-9)^2+(6-2)^2)$

$=sqrt(3^2+5^2+4^2)$

$=sqrt(9+25+16)$

$=sqrt50$

$=7.07$

We apply the equation of motion

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

$u=0$

so,

$d=1/2at^2$

$t^2=(2d)/a=(2*7.07)/(1/3)$

$=42.43$

$t=sqrt(42.43)=6.51s$

An object is at rest at (1 ,9 ,2 )(1 ,9 ,2 ) and constantly accelerates at a rate of 1/3 m/s1/3 m/s as it moves to point B. If point B is at (4 ,4 ,6 )(4 ,4 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.