An object is at rest at #(8 ,7 ,3 )# and constantly accelerates at a rate of #1/4 m/s^2# as it moves to point B. If point B is at #(6 ,3 ,4 )#, 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 · 2018-07-10T05:21:10

The time is #=6.05s#

The distance #AB# is

#d_(AB)=sqrt((6-8)^2+(3-7)^2+(4-3)^2)#

#=sqrt(2^2+4^2+1^2)#

#=sqrt(4+16+1)#

#=sqrt(21)m#

The acceleration is #a=1/4ms^-2#

The initial velocity #u=0#

Apply the equation of motion

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

#sqrt(21)=0+1/2*1/4*t^2#

#t^2=8sqrt(21)#

#t=sqrt(8sqrt(21))=6.05s#

The time is #=6.05s#