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:

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

$t~~3.98" s"$

An object is at rest at (9 ,7 ,5 )(9 ,7 ,5 ) and constantly accelerates at a rate of 5/4 m/s^25/4 m/s^2 as it moves to point B. If point B is at (1 ,2 ,2 )(1 ,2 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.