An object is at rest at #(2 ,9 ,5 )# and constantly accelerates at a rate of #7/6 m/s# as it moves to point B. If point B is at #(6 ,3 ,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 · 2018-05-30T08:13:33

The time is #=3.58s#

The distance #AB# is

#AB=sqrt((6-2)^2+(3-9)^2+(7-5)^2)=sqrt(16+36+4)=sqrt(56)m#

Apply the equation of motion

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

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

The acceleration is #a=7/6ms^-2#

Therefore,

#sqrt56=0+1/2*7/6*t^2#

#t^2=12/7sqrt56#

#t=sqrt(12/7sqrt56)=3.58s#