An object is at rest at $(8 ,2 ,5 )$ and constantly accelerates at a rate of $7/4 m/s^2$ as it moves to point B. If point B is at $(6 ,5 ,7 )$ , 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 · 2017-04-07T06:55:30

The time is $=4.71s$

The distance between the 2 points $A(8,2,5)$ and $B(6,5,7)$ is

$s=sqrt((6-8)^2+(5-2)^2+(7-5)^2)$

$s=sqrt(4+9+4)$

$s=sqrt17m$

We apply the equation of motion

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

initial velocity, $u=0ms^-1$

acceleration, $a=7/4ms^-2$

distance, $s=sqrt17m$

so,

$sqrt17=0+1/2*7/4*t$

$t=8/7sqrt17=4.71s$

An object is at rest at (8 ,2 ,5 )(8 ,2 ,5 ) and constantly accelerates at a rate of 7/4 m/s^27/4 m/s^2 as it moves to point B. If point B is at (6 ,5 ,7 )(6 ,5 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.