An object is at rest at #(2 ,1 ,5 )# and constantly accelerates at a rate of #2 m/s# as it moves to point B. If point B is at #(6 ,7 ,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 · 2018-04-21T06:06:31

The time is #=2.74s#

The distance #AB# is

#AB=sqrt((6-2)^2+(7-1)^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=2ms^-2#

Therefore,

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

#t^2=sqrt56#

#t=sqrt(sqrt56)=2.74s#