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

1 Answer
David G.
May 21, 2016

First step is to find the distance between the points, which is approximately #9.2# #m#. Then the time taken can be calculated, as shown below, to be #6.8# #s#.

Explanation:

Distance between the points:

#r=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#
#=sqrt((6-2)^2+(9-1)^2+(7-1)^2)=sqrt(4^2+8^2+6^2)#
#=sqrt(16+64+4)=sqrt(84)~~9.2# #m#

Finding the time taken, given that the object is at rest (#u=0#):

#d=ut+1/2at^2=1/2at^2# (when #u=0#)

Rearranging:

#t=sqrt((2d)/a)=sqrt((2*9.2)/(2/5))=sqrt46~~6.8# #s#

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