An object is at rest at #(1 ,2 ,9 )# and constantly accelerates at a rate of #1 m/s^2# as it moves to point B. If point B is at #(6 ,1 ,3 )#, 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 · 2018-03-20T06:44:15

The time is #=4.0s#

The distance #AB# is

#AB=sqrt((6-1)^2+(1-2)^2+(3-9)^2)=sqrt(25+1+36)=sqrt(62)m#

Apply the equation of motion

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

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

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

Therefore,

#sqrt62=0+1/2*1*t^2#

#t^2=2*sqrt62#

#t=sqrt(2*sqrt62)=4.0s#