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 #(1 ,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 · 2017-12-12T06:26:28

The time is #=8.06s#

The distance #AB# is

#AB=sqrt((1-8)^2+(3-7)^2+(2-3)^2)=sqrt(49+16+1)=(sqrt66)m#

Apply the equation of motion

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

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

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

Therefore,

#sqrt66=0+1/2*1/4*t^2#

#t^2=8sqrt66#

#t=sqrt(8sqrt66)=8.06s#