An object is at rest at $(3, 8, 8)$ $(3 ,8 ,8 )$ and constantly accelerates at a rate of $\frac{5}{4} \frac{m}{s^{2}}$ $5/4 m/s^2$ 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.

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An object is at rest at $(3, 8, 8)$ $(3 ,8 ,8 )$ and constantly accelerates at a rate of $\frac{5}{4} \frac{m}{s^{2}}$ $5/4 m/s^2$ 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.

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Answer 1 · 2018-07-26T01:49:15

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

Explanation:

Begin the the equation

$x = \frac{1}{2} a t^{2} + v_{i} t$ $x = 1/2at^2 + v_it$

Which simplifies since $v_{i} = 0 \frac{m}{s}$ $v_i = 0 m /s$

$x = \frac{1}{2} a t^{2} \Rightarrow t^{2} = \frac{2 x}{a} \Rightarrow t = \sqrt{\frac{2 x}{a}}$ $x = 1/2at^2 => t^2 = (2x)/a => t = sqrt((2x)/a)$

Finding the distance, use the formula for Euclidean distance:

$x = \sqrt{{(3 - 2)}^{2} + {(8 - 9)}^{2} + {(8 - 5)}^{2}} m$ $x = sqrt((color(red)3-color(blue)2)^2 + (color(red)8 - color(blue)9)^2 + (color(red)8 - color(blue)5)^2) m$

$x = \sqrt{11} m$ $x = sqrt(11) m$

Substituting $x = \sqrt{11} m$ $x = sqrt(11) m$ and $a = \frac{5}{4} \frac{m}{s^{2}}$ $a = 5/4 m/s^2$ in the formula:

$t = \sqrt{\frac{2 \sqrt{11} m}{\frac{5}{4} \frac{m}{s^{2}}}}$ $t = sqrt((2sqrt11 m)/(5/4 m/s^2))$

$t = \sqrt{\frac{8 \sqrt{11}}{5}} s$ $t = sqrt((8sqrt11)/5) s$

$t \approx 2.3 s$ $t ~~ 2.3 s$

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An object is at rest at $(3, 8, 8)$ $(3 ,8 ,8 )$ and constantly accelerates at a rate of $\frac{5}{4} \frac{m}{s^{2}}$ $5/4 m/s^2$ 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.

1 Answer

Explanation:

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An object is at rest at (3,8,8)(3 ,8 ,8 ) and constantly accelerates at a rate of 54ms25/4 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.

1 Answer

Explanation:

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An object is at rest at $(3, 8, 8)$ $(3 ,8 ,8 )$ and constantly accelerates at a rate of $\frac{5}{4} \frac{m}{s^{2}}$ $5/4 m/s^2$ 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.