An object is at rest at #(9 ,7 ,5 )# and constantly accelerates at a rate of #5/4 m/s^2# as it moves to point B. If point B is at #(1 ,2 ,2 )#, 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 · 2017-10-12T15:57:21

#t~~3.98" s"#

Compute the distance from point A to point B:

#d = sqrt((9-1)^2+(7-2)^2+(5-2)^2)#

#d = 7sqrt2" m"#

To find the time, #t#, taken to travel a distance, #d#, given the constant acceleration, we shall use the equation:

#d = 1/2at^2#

Solve for t:

#t = sqrt(2d/a)#

Substitute #d = 7sqrt2" m"# and #a = 5/4" m/s"^2# into the equation:

#t = sqrt(2(7sqrt2" m")/(5/4" m/s"^2))#

#t~~3.98" s"#