An object is at rest at #(7 ,6 ,4 )# and constantly accelerates at a rate of #7/4 m/s^2# as it moves to point B. If point B is at #(5 ,1 ,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 · 2018-01-30T10:42:52

The time is #=2.65s#

The distance #AB# is

#AB=sqrt((5-7)^2+(1-6)^2+(7-4)^2)=sqrt(4+25+9)=sqrt(38)m#

Apply the equation of motion

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

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

The acceleration is #a=7/4ms^-2#

Therefore,

#sqrt38=0+1/2*7/4*t^2#

#t^2=8/7*sqrt38#

#t=sqrt(8/7*sqrt38)=2.65s#