An object is at rest at $(2 ,1 ,3 )$ and constantly accelerates at a rate of $1 m/s^2$ as it moves to point B. If point B is at $(9 ,3 ,5 )$ , 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 · 2017-03-27T18:41:56

The time is $=3.89s$

The distance between the 2 points $A=(2,1,3)$ and $B=(9,3,5)$ is

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

$=sqrt(49+4+4)$

$=sqrt57$

$a(t)=1$

The velocity is

$v(t)=int_0^t1dt=t$

The distance is

$s=int_0^t tdt=1/2t^2$

This is equal to

sqrt57=1/2t^2

$t^2=2sqrt57=15.1$

So,

$t=sqrt15.1=3.89s$

An object is at rest at (2 ,1 ,3 )(2 ,1 ,3 ) 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 (9 ,3 ,5 )(9 ,3 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.