An object is at rest at $(3, 7, 8)$ $(3 ,7 ,8 )$ 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 $(1, 9, 2)$ $(1 ,9 ,2 )$ , 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 $(3, 7, 8)$ $(3 ,7 ,8 )$ 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 $(1, 9, 2)$ $(1 ,9 ,2 )$ , 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 · 2018-01-12T06:59:37

The time is $= 3.26 s$ $=3.26s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(1 - 3)}^{2} + {(9 - 7)}^{2} + {(2 - 8)}^{2}} = \sqrt{4 + 4 + 36} = \sqrt{44} m$ $AB=sqrt((1-3)^2+(9-7)^2+(2-8)^2)=sqrt(4+4+36)=sqrt(44)m$

Apply the equation of motion

$s = u t + \frac{1}{2} a t^{2}$ $s=ut+1/2at^2$

The initial velocity is $u = 0 m s^{- 1}$ $u=0ms^-1$

The acceleration is $a = \frac{5}{4} m s^{- 2}$ $a=5/4ms^-2$

Therefore,

$\sqrt{44} = 0 + \frac{1}{2} \cdot \frac{5}{4} \cdot t^{2}$ $sqrt44=0+1/2*5/4*t^2$

$t^{2} = \frac{8}{5} \cdot \sqrt{44}$ $t^2=8/5*sqrt44$

$t = \sqrt{\frac{8}{5} \cdot \sqrt{44}} = 3.26 s$ $t=sqrt(8/5*sqrt44)=3.26s$

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An object is at rest at $(3, 7, 8)$ $(3 ,7 ,8 )$ 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 $(1, 9, 2)$ $(1 ,9 ,2 )$ , 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 (3,7,8)(3 ,7 ,8 ) and constantly accelerates at a rate of 54ms25/4 m/s^2 as it moves to point B. If point B is at (1,9,2)(1 ,9 ,2 ), 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 $(3, 7, 8)$ $(3 ,7 ,8 )$ 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 $(1, 9, 2)$ $(1 ,9 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.