An object is at rest at #(1 ,7 ,4 )# and constantly accelerates at a rate of #5/4 m/s^2# as it moves to point B. If point B is at #(8 ,5 ,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 · 2017-06-07T06:24:47

The time is #=3.48s#

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((8-1)^2+(5-7)^2+(6-4)^2)#

#=sqrt(7^2+2^2+2^2)#

#=sqrt(49+4+4)#

#=sqrt57#

#=7.55m#

We apply the equation of motion

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

#u=0#

so,

#d=1/2at^2#

#a=5/4ms^-2#

#t^2=(2d)/a=(2*7.55)/(5/4)#

#=12.08s^2#

#t=sqrt(12.08)=3.48s#