An object is at rest at #(4 ,8 ,3 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(3 ,5 ,7 )#, 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 · 2018-01-31T10:43:51

The time is #=2.77s#

The distance #AB# is

#AB=sqrt((3-4)^2+(5-8)^2+(7-3)^2)=sqrt(1+9+16)=sqrt(26)m#

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,

#sqrt26=0+1/2*4/3*t^2#

#t^2=3/2*sqrt26#

#t=sqrt(3/2*sqrt26)=2.77s#