An object is at rest at #(9 ,1 ,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 ,8 ,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 · 2017-08-11T06:18:10

The time is #=15.7s#

The distance #AB# is

#AB=sqrt((6-9)^2+(8-1)^2+(2-3)^2)=sqrt((-3)^2+(7)^2+(-1)^2)#

#=sqrt(9+49+1)=sqrt59m#

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

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

We apply the equation of motion

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

So,

#sqrt59=0+1/2*(1/4)^2*t^2#

#t^2=32sqrt59#

#t=sqrt(32sqrt59)=15.7s#