An object is at rest at $(1 ,7 ,4 )$ and constantly accelerates at a rate of $5/4 m/s^2$ as it moves to point B. If point B is at $(8 ,5 ,6 )$ , 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 · 2017-06-07T06:24:47

The time is $=3.48s$

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

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

$d=AB= sqrt((8-1)^2+(5-7)^2+(6-4)^2)$

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

$=sqrt(49+4+4)$

$=sqrt57$

$=7.55m$

We apply the equation of motion

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

$u=0$

so,

$d=1/2at^2$

$a=5/4ms^-2$

$t^2=(2d)/a=(2*7.55)/(5/4)$

$=12.08s^2$

$t=sqrt(12.08)=3.48s$

An object is at rest at (1 ,7 ,4 )(1 ,7 ,4 ) 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 ,5 ,6 )(8 ,5 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.