An object is at rest at #(8 ,2 ,5 )# 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 ,7 )#, 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 · 2017-04-07T06:55:30

The time is #=4.71s#

The distance between the 2 points #A(8,2,5)# and #B(6,5,7)# is

#s=sqrt((6-8)^2+(5-2)^2+(7-5)^2)#

#s=sqrt(4+9+4)#

#s=sqrt17m#

We apply the equation of motion

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

initial velocity, #u=0ms^-1#

acceleration, #a=7/4ms^-2#

distance, #s=sqrt17m#

so,

#sqrt17=0+1/2*7/4*t#

#t=8/7sqrt17=4.71s#