An object is at rest at #(2 ,2 ,8 )# and constantly accelerates at a rate of #1/5 m/s# as it moves to point B. If point B is at #(6 ,3 ,2 )#, 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 · 2018-02-21T07:15:50

The time is #=12.07s#

The distance #AB# is

#AB=sqrt((6-2)^2+(3-2)^2+(2-8)^2)=sqrt(16+1+36)=sqrt(53)m#

Apply the equation of motion

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

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

The acceleration is #a=1/5ms^-2#

Therefore,

#sqrt53=0+1/2*1/5*t^2#

#t^2=20*sqrt53#

#t=sqrt(20*sqrt53)=12.07s#