An object is at rest at #(2 ,4 ,1 )# and constantly accelerates at a rate of #2/5 m/s# as it moves to point B. If point B is at #(6 ,6 ,7 )#, 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 · 2017-05-08T12:11:57

The time is #=6.12s#

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

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

#=sqrt(16+4+36)#

#=sqrt56#

#=7.48#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#t^2=(2d)/a=(2*7.48)/(2/5)#

#=37.42#

#t=sqrt(37.42)=6.12s#