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 ,3 )#, 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 · 2016-03-30T12:47:14

#t=3,43 "s"#

#"distance between (1,7,4) and (8,5,3):"#

#s=sqrt((8-1)^2+(5-7)^2+(3-4)^2)#

#s=sqrt(7^2+(-2)^2+(-1)^2)#

#s=sqrt(49+4+1)#

#s=sqrt54#

#s=7,35 " m"#

#a=5/4=1,25 " "m/s^2#

#t=?#

#s=1/2*a*t^2#

#t^2=2*s/a#

#t^2=(2*7,35)/(1,25)#

#t^2=11,76#

#sqrt (t^2)=sqrt (11,76)#

#t=3,43 "s"#