An object is at rest at $(2 ,9 ,5 )$ and constantly accelerates at a rate of $1/6 m/s$ as it moves to point B. If point B is at $(6 ,2 ,7 )$ , 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 · 2016-04-08T16:48:18

$color(blue)(=>t = 9.984" seconds ")$ to 3 decimal places

$color(blue)("Determine distance between points")$

Let point start be $P_s->(x_1,y_1,z_1) ->( 2,9,5)$
Let point end be $P_e->(x_2,y_2,z_2)->(6,2,7)$

Let direct distance between $P_s->P_e$ be $d$

Then by using Pythagoras we have:

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

$d=sqrt([6-2]^2+[2-9]^2+[7-5]^2)$

$color(blue)(d=sqrt(69)" metres")$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using the standard form equation for distance

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

Where
distance $->s=sqrt(69)$
initial velocity $->u=0$
acceleration $-> a = 1/6$

$=> sqrt(69)=(1/2)(1/6)t^2$

$=>t^2=12sqrt(69)$

$color(blue)(=>t = 9.984" seconds ")$ to 3 decimal places

An object is at rest at (2 ,9 ,5 )(2 ,9 ,5 ) and constantly accelerates at a rate of 1/6 m/s1/6 m/s as it moves to point B. If point B is at (6 ,2 ,7 )(6 ,2 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.