An object is at rest at #(3 ,8 ,8 )# and constantly accelerates at a rate of #5/4 m/s^2# as it moves to point B. If point B is at #(2 ,9 ,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 · 2018-07-26T01:49:15

It will take the object approximately #2.3s# to reach point B.

Begin the the equation

#x = 1/2at^2 + v_it#

Which simplifies since #v_i = 0 m /s#

#x = 1/2at^2 => t^2 = (2x)/a => t = sqrt((2x)/a)#

Finding the distance, use the formula for Euclidean distance:

#x = sqrt((color(red)3-color(blue)2)^2 + (color(red)8 - color(blue)9)^2 + (color(red)8 - color(blue)5)^2) m#

#x = sqrt(11) m#

Substituting #x = sqrt(11) m# and #a = 5/4 m/s^2# in the formula:

#t = sqrt((2sqrt11 m)/(5/4 m/s^2))#

#t = sqrt((8sqrt11)/5) s#

#t ~~ 2.3 s#