An object is at rest at $(3 ,5 ,1 )$ and constantly accelerates at a rate of $4/3 m/s^2$ as it moves to point B. If point B is at $(7 ,9 ,2 )$ , 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 · 2017-03-17T15:43:26

The time taken is $=2.94s$

We are going to apply the following equation of motion :

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

$u_0=0$

So,

$s=1/2at^2$

$a=4/3ms^-2$

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,

$A=(3,5,1)$ and $B=(7,9,2)$

So,

$s=sqrt((7-3)^2+(9-5)^2+(2-1)^2)$

$=sqrt(16+16+1)$

$=sqrt33$

From the equation of motion,

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

$t^2=(2*sqrt33)/(4/3)=8.62$

$t=sqrt8.62=2.94s$

An object is at rest at (3 ,5 ,1 )(3 ,5 ,1 ) and constantly accelerates at a rate of 4/3 m/s^24/3 m/s^2 as it moves to point B. If point B is at (7 ,9 ,2 )(7 ,9 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.