An object is at rest at #(8 ,6 ,9 )# and constantly accelerates at a rate of #1 m/s# as it moves to point B. If point B is at #(6 ,4 ,3 )#, 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 · 2017-06-11T06:29:00

The time is #=3.64s#

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((6-8)^2+(4-6)^2+(3-9)^2)#

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

#=sqrt(4+4+36)#

#=sqrt44#

#=6.63m#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#a=5/4ms^-2#

#t^2=(2d)/a=(2*6.63)/(1)#

#=13.27s^2#

#t=sqrt(13.27)=3.64s#