An object is at rest at #(8 ,1 ,7 )# and constantly accelerates at a rate of #7/4 m/s^2# as it moves to point B. If point B is at #(6 ,5 ,2 )#, 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 · 2017-04-24T13:05:44

The time is #=2.77s#

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

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

#=sqrt(4+16+25)#

#=sqrt45#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#t^2=(2d)/a=(2sqrt45)/(7/4)#

#=7.67#

#t=sqrt(7.67)=2.77s#