An object is at rest at #(5 ,2 ,1 )# and constantly accelerates at a rate of #2/3 m/s# as it moves to point B. If point B is at #(4 ,9 ,8 )#, 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 · 2018-04-02T06:50:49

The time is #=5.46s#

The distance #AB# is

#AB=sqrt((4-5)^2+(9-2)^2+(8-1)^2)=sqrt(1+49+49)=sqrt(99)m#

Apply the equation of motion

#s=ut+1/2at^2#

The initial velocity is #u=0ms^-1#

The acceleration is #a=2/3ms^-2#

Therefore,

#sqrt99=0+1/2*2/3*t^2#

#t^2=3*sqrt99#

#t=sqrt(3*sqrt99)=5.46s#