An object is at rest at #(1 ,5 ,5 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(3 ,6 ,4 )#, 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 · 2017-11-26T07:34:26

The time is #=1.92s#

The distance #AB# is

#AB=sqrt((3-1)^2+(6-5)^2+(4-5)^2)=sqrt(4+1+1)=sqrt6m#

Apply the equation of motion

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

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

The acceleration is #a=4/3ms^-2#

Therefore,

#sqrt6=0*1/2*4/3*t^2#

#t^2=3/2sqrt6#

#t=sqrt(3/2sqrt6)=1.92s#