An object is at rest at #(3 ,7 ,2 )# and constantly accelerates at a rate of #7/5 m/s^2# as it moves to point B. If point B is at #(5 ,0 ,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 · 2018-01-04T14:32:06

The time is #=3.8s#

The distance #AB# is

#AB=sqrt((5-3)^2+(0-7)^2+(9-2)^2)=sqrt(4+49+49)=(sqrt102)m#

Apply the equation of motion

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

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

The acceleration is #a=7/5ms^-2#

Therefore,

#sqrt(102)=0+1/2*7/5*t^2#

#t^2=10/7sqrt102#

#t=sqrt(10/7sqrt102)=3.8s#