An object is at rest at #(2 ,9 ,8 )# and constantly accelerates at a rate of #1/5 m/s# as it moves to point B. If point B is at #(6 ,2 ,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 · 2017-04-08T13:09:04

The time is #=10.02s#

The distance between the points #A=(x_A,y_A,z_A)# and the point #B=(x_B,y_B,z_B)# is

#AB=sqrt((x_B-x_A)^2+(y_B-y_A)^2+(z_B-z_A)^2)#

#d=AB= sqrt((6-2)^2+(2-9)^2+(2-8)^2)#

#=sqrt(4^2+7^2+6^2)#

#=sqrt(16+49+36)#

#=sqrt101#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#t^2=(2d)/a=(2sqrt101)/(1/5)#

#=100.5#

#t=sqrt(100.5)=10.02s#