An object is at rest at $(2 ,1 ,5 )$ and constantly accelerates at a rate of $2 m/s$ as it moves to point B. If point B is at $(6 ,7 ,5 )$ , 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 · 2017-07-02T15:06:13

The time is $=2.69s$

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

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

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

$=sqrt(4^2+6^2+0^2)$

$=sqrt(16+36+0)$

$=sqrt52$

$=7.21m$

We apply the equation of motion

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

$u=0$

so,

$d=1/2at^2$

$a=2ms^-2$

$t^2=(2d)/a=(2*7.21)/(2)$

$=7.21s^2$

$t=sqrt(7.21)=2.69s$

An object is at rest at (2 ,1 ,5 )(2 ,1 ,5 ) and constantly accelerates at a rate of 2 m/s2 m/s as it moves to point B. If point B is at (6 ,7 ,5 )(6 ,7 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.