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