An object is at rest at $(7 ,4 ,2 )$ and constantly accelerates at a rate of $4/5 m/s$ as it moves to point B. If point B is at $(3 ,1 ,9 )$ , 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 · 2016-04-21T10:39:48

Approximately 4.6 seconds

Assuming that the rate of acceleration is $4/5 m/(sec^2)$ (that the "squared" was left off the "seconds" of the acceleration.)

Distance between $(7,4,2)$ and $(3,1,9)$
$color(white)("XXX")d=sqrt((7-3)^2+(4-1)^2+(2-9)^2)$
$color(white)("XXXX")=sqrt(74)$

The relationship between distance, acceleration (from zero), and time is given by the formula:
$color(white)("XXX")d=1/2a*t^2$

Therefore
$color(white)("XXX")sqrt(74)m=1/(cancel(2)) * cancel(4)^2/5 m/cancel(sec^2) * (t^2 cancel(sec^2))color(white)("/x")$

$color(white)("XXX")t^2=(5sqrt(74))/2$

(using a calculator)
$color(white)("XXX")t=sqrt((5sqrt(74))/2)~~4.637436$

An object is at rest at (7 ,4 ,2 )(7 ,4 ,2 ) and constantly accelerates at a rate of 4/5 m/s4/5 m/s as it moves to point B. If point B is at (3 ,1 ,9 )(3 ,1 ,9 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.