An object is at rest at #(4 ,5 ,1 )# and constantly accelerates at a rate of #5/3 m/s^2# as it moves to point B. If point B is at #(7 ,2 ,6 )#, 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 · 2017-05-03T05:16:40

The time is #=2.81s#

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((7-4)^2+(2-5)^2+(6-1)^2)#

#=sqrt(3^2+3^2+5^2)#

#=sqrt(9+9+25)#

#=sqrt43#

#=6.56#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#t^2=(2d)/a=(2*6.56)/(5/3)#

#=7.87#

#t=sqrt(7.87)=2.81s#