An object is at rest at $(8 ,2 ,9 )$ and constantly accelerates at a rate of $3 m/s$ as it moves to point B. If point B is at $(6 ,7 ,3 )$ , 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 · 2017-03-19T13:28:20

The time is $=2.32s$

We are going to apply the following equation of motion :

$s=u_0t+1/2at^2$

$u_0=0$

So,

$s=1/2at^2$

$a=3ms^-2$

The distance between 2 points $A=(x_1,y_1,z_1)$ and $B=(x_2.y_2.z_2)$ is

$=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$

Here,

$A=(8,2,9)$ and $B=(6,7,3)$

So,

$s=sqrt((6-8)^2+(7-2)^2+(3-9)^2)$

$=sqrt(4+25+36)$

$=sqrt65$

From the equation of motion,

$t^2=(2s)/a$

$t^2=(2*sqrt65)/(3)=5.37$

$t=sqrt5.37=2.32s$

An object is at rest at (8 ,2 ,9 )(8 ,2 ,9 ) and constantly accelerates at a rate of 3 m/s3 m/s as it moves to point B. If point B is at (6 ,7 ,3 )(6 ,7 ,3 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.