An object is at rest at #(1 ,6 ,9 )# and constantly accelerates at a rate of #1# # ms^-2# as it moves to point B. If point B is at #(6 ,4 ,3 )#, 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 · 2017-06-07T12:33:57

The distance is #8.06# #m#, and the object will take #4.01# #s# to travel this distance.

First we need to find the distance between the two points:

#s=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

#s=sqrt((6-1)^2+(4-6)^2+(3-9)^2)#

#s=sqrt((5)^2+(-2)^2+(-6)^2)#

#s=sqrt(25+4+36) = sqrt(65) = 8.06# #m# (assuming the units are in metres)

Then we can use #s = ut + 1/2 at^2#

The initial velocity, #u#, is equal to #0#, so the first term disappears.

#s = 1/2 at^2#

Rearranging:

#t=sqrt((2s)/a)=sqrt((2(8.06))/1)=4.01# #s#