An object is at rest at #(2 ,4 ,1 )# and constantly accelerates at a rate of #4/5# # ms^-1# as it moves to point B. If point B is at #(6 ,6 ,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 · 2016-05-07T09:39:54

The distance between the points is #7.48# #m#.

The time taken is #t=sqrt(d/a)=sqrt(7.48/0.8)~~3.06# #s#.

First find the distance between the points:

#l=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#
#=sqrt((6-2)^2+(6-4)^2+(7-1)^2)=sqrt(16+4+36)#
#=sqrt56~~7.48# #m#

An acceleration of #4/5# can be expressed as #0.8#.

#d=ut+at^2# can be rearranged to #t=sqrt(d/a)# when #u=0# (which it is in this case).