An object is at rest at #(8 ,1 ,2 )# and constantly accelerates at a rate of #3 m/s# as it moves to point B. If point B is at #(6 ,7 ,5 )#, 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 · 2017-04-26T06:43:33

The time is #=2.16s#

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

#=sqrt(2^2+6^2+3^2)#

#=sqrt(4+36+9)#

#=sqrt49#

#=7#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#t^2=(2d)/a=(2*7)/(3)#

#=4.67#

#t=sqrt(4.67)=2.16s#