An object is at rest at #(1 ,3 ,9 )# and constantly accelerates at a rate of #7/4# #ms^-2# as it moves to point B. If point B is at #(2 ,5 ,6 )#, 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 · 2016-03-23T00:23:34

The distance between the points (calculated below) is #3.74# #m#. Then #d=ut+1/2at^2=0(t)+1/2(7/4)t^2.# Rearranging, #7/8t^2=3.74 to t = 2.1 s#.

To find the distance between the points:

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#
#=sqrt((2-1)^2+(5-3)^2+(6-9)^2)#
#=sqrt(1+4+9)=sqrt14~~3.74# #m#.