An object is at rest at #(7 ,3 ,9 )# and constantly accelerates at a rate of #7/4 m/s^2# as it moves to point B. If point B is at #(2 ,5 ,0 )#, 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 · 2018-06-10T06:15:33

The time is #=3.46s#

The distance #AB# is

#||vec(AB)||=sqrt((2-7)^2+(5-3)^2+(0-9)^2)=sqrt(25+4+81)=sqrt(110)m#

Apply the equation of motion

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

The initial velocity is #u=0ms^-1#

The acceleration is #a=7/4ms^-2#

Therefore,

#sqrt110=0+1/2*7/4*t^2#

#t^2=8/7sqrt110#

#t=sqrt(8/7sqrt110)=3.46s#

The time is #=3.46s#