An object is at rest at #(5 ,2 ,8 )# and constantly accelerates at a rate of #1/5 m/s# as it moves to point B. If point B is at #(6 ,3 ,2 )#, 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 · 2017-11-26T07:37:51

The time is #=7.85s#

The distance #AB# is

#AB=sqrt((6-5)^2+(3-2)^2+(2-8)^2)=sqrt(1+1+36)=(sqrt38)m#

Apply the equation of motion

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

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

The acceleration is #a=1/5ms^-2#

Therefore,

#sqrt38=0*1/2*1/5*t^2#

#t^2=10sqrt38#

#t=sqrt(10sqrt38)=7.85s#