An object is at rest at #(1 ,9 ,2 )# and constantly accelerates at a rate of #1/3 m/s# as it moves to point B. If point B is at #(4 ,4 ,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 · 2017-04-29T05:51:57

The time is #=6.51s#

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((4-1)^2+(4-9)^2+(6-2)^2)#

#=sqrt(3^2+5^2+4^2)#

#=sqrt(9+25+16)#

#=sqrt50#

#=7.07#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#t^2=(2d)/a=(2*7.07)/(1/3)#

#=42.43#

#t=sqrt(42.43)=6.51s#