An object is at rest at $(6 ,2 ,8 )$ and constantly accelerates at a rate of $1 m/s^2$ as it moves to point B. If point B is at $(3 ,7 ,5 )$ , 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 · 2017-06-17T06:11:39

The time is $=3.62s$

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

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

$d=AB= sqrt((3-6)^2+(7-2)^2+(5-8)^2)$

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

$=sqrt(9+25+9)$

$=sqrt43$

$=6.56m$

We apply the equation of motion

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

$u=0$

so,

$d=1/2at^2$

$a=1ms^-2$

$t^2=(2d)/a=(2*6.56)/(1)$

$=13.11s^2$

$t=sqrt(13.11)=3.62s$

An object is at rest at (6 ,2 ,8 )(6 ,2 ,8 ) and constantly accelerates at a rate of 1 m/s^21 m/s^2 as it moves to point B. If point B is at (3 ,7 ,5 )(3 ,7 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.