An object is at rest at #(2 ,9 ,5 )# and constantly accelerates at a rate of #7/6 m/s# as it moves to point B. If point B is at #(6 ,2 ,7 )#, 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 · 2017-07-24T16:08:02

The time is #=3.77s#

The distance is

#s=sqrt((6-2)^2+(2-9)^2+(7-5)^2)#

#=sqrt(16+49+4)#

#=sqrt69#

#a=7/6ms^-2#

The initial velocity is

#u=0ms^-1#

We apply the equation of motion

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

#t^2=(2s)/a#

#=(2*sqrt69)/(7/6)#

#=14.24#

So,

#t=sqrt14.24=3.77s#