An object is at rest at #(4 ,5 ,1 )# and constantly accelerates at a rate of #5/3 m/s^2# as it moves to point B. If point B is at #(7 ,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 · 2017-12-03T08:55:53

The time is #=2.65s#

The distance #AB# is

#AB=sqrt((7-4)^2+(5-5)^2+(6-1)^2)=sqrt(9+0+25)=(sqrt34)m#

Apply the equation of motion

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

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

The acceleration is #a=5/3ms^-2#

Therefore,

#sqrt34=0*1/2*5/3*t^2#

#t^2=6/5sqrt34#

#t=sqrt(6/5sqrt34)=2.65s#