An object is at rest at $(9 ,7 ,5 )$ and constantly accelerates at a rate of $5/4 m/s^2$ as it moves to point B. If point B is at $(8 ,2 ,6 )$ , 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 · 2017-06-04T06:59:21

The time is $=2.88s$

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

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

$d=AB= sqrt((8-9)^2+(2-7)^2+(6-5)^2)$

$=sqrt(1^2+5^2+1^2)$

$=sqrt(1+25+1)$

$=sqrt27$

$=5.196m$

We apply the equation of motion

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

$u=0$

so,

$d=1/2at^2$

$a=5/4ms^-2$

$t^2=(2d)/a=(2*5.196)/(5/4)$

$=8.31s^2$

$t=sqrt(8.31)=2.88s$

An object is at rest at (9 ,7 ,5 )(9 ,7 ,5 ) and constantly accelerates at a rate of 5/4 m/s^25/4 m/s^2 as it moves to point B. If point B is at (8 ,2 ,6 )(8 ,2 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.