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.

Question

1688 views around the world

You can reuse this answer
Creative Commons License

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:

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

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

$t ~~ 2.3 s$

An object is at rest at (3 ,8 ,8 )(3 ,8 ,8 ) 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 (2 ,9 ,5 )(2 ,9 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.