An object is at rest at #(6 ,2 ,8 )# and constantly accelerates at a rate of #1 m/s^2# as it moves to point B. If point B is at #(3 ,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 · 2017-06-17T06:11:39

The time is #=3.62s#

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((3-6)^2+(7-2)^2+(5-8)^2)#

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

#=sqrt(9+25+9)#

#=sqrt43#

#=6.56m#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#a=1ms^-2#

#t^2=(2d)/a=(2*6.56)/(1)#

#=13.11s^2#

#t=sqrt(13.11)=3.62s#