An object is at rest at #(4 ,1 ,8 )# and constantly accelerates at a rate of #7/5 m/s^2# as it moves to point B. If point B is at #(2 ,9 ,1 )#, 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 · 2017-11-29T19:13:22

The time is #=3.93s#

The distance #AB# is

#AB=sqrt((2-4)^2+(9-1)^2+(1-8)^2)=sqrt(4+64+49)=(sqrt117)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,

#sqrt117=0*1/2*7/5*t^2#

#t^2=10/7sqrt117#

#t=sqrt(10/7sqrt117)=3.93s#