An object is at rest at #(2 ,1 ,5 )# and constantly accelerates at a rate of #2 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 · 2017-07-02T15:06:13

The time is #=2.69s#

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

#=sqrt(4^2+6^2+0^2)#

#=sqrt(16+36+0)#

#=sqrt52#

#=7.21m#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#a=2ms^-2#

#t^2=(2d)/a=(2*7.21)/(2)#

#=7.21s^2#

#t=sqrt(7.21)=2.69s#