An object is at rest at #(5 ,2 ,1 )# and constantly accelerates at a rate of #2/5 m/s# as it moves to point B. If point B is at #(6 ,9 ,2 )#, 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 · 2018-07-03T06:22:13

The time is #=5.98s#

The distance #AB# is

#d_(AB)=sqrt((6-5)^2+(9-2)^2+(2-1)^2)#

#=sqrt(1^2+7^2+1^2)#

#=sqrt(1+49+1)#

#=sqrt(51)m#

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

The initial velocity #u=0#

Apply the equation of motion

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

#sqrt(51)=0+1/2*2/5*t^2#

#t^2=5sqrt(51)#

#t=sqrt(5sqrt(51))=5.98s#

The time is #=5.98s#