An object is at rest at #(2 ,1 ,3 )# and constantly accelerates at a rate of #1 m/s^2# as it moves to point B. If point B is at #(9 ,3 ,5 )#, 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 · 2017-03-27T18:41:56

The time is #=3.89s#

The distance between the 2 points #A=(2,1,3)# and #B=(9,3,5)# is

#d=sqrt((9-2)^2+(3-1)^2+(5-3)^2)#

#=sqrt(49+4+4)#

#=sqrt57#

#a(t)=1#

The velocity is

#v(t)=int_0^t1dt=t#

The distance is

#s=int_0^t tdt=1/2t^2#

This is equal to

sqrt57=1/2t^2

#t^2=2sqrt57=15.1#

So,

#t=sqrt15.1=3.89s#