An object is at rest at #(2 ,4 ,2 )# and constantly accelerates at a rate of #4/5 m/s# as it moves to point B. If point B is at #(3 ,6 ,9 )#, 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 · 2017-09-14T09:30:43

The time is #=4.79s#

The distance #AB# is

#AB=sqrt((3-2)^2+(6-4)^2+(9-2)^2)=sqrt((1)^2+(2)^2+(7)^2)#

#=sqrt(1+4+49)=sqrt54m#

The acceleration is #a=4/5ms^-2#

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

We apply the equation of motion

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

So,

#sqrt54=0+1/2*(4/5)^2*t^2#

#t^2=50/16sqrt54#

#t=sqrt(50/16sqrt54)=4.79s#