An object is at rest at $(5, 2, 1)$ $(5 ,2 ,1 )$ and constantly accelerates at a rate of $\frac{2}{3} \frac{m}{s}$ $2/3 m/s$ as it moves to point B. If point B is at $(4, 9, 8)$ $(4 ,9 ,8 )$ , 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 $(5, 2, 1)$ $(5 ,2 ,1 )$ and constantly accelerates at a rate of $\frac{2}{3} \frac{m}{s}$ $2/3 m/s$ as it moves to point B. If point B is at $(4, 9, 8)$ $(4 ,9 ,8 )$ , 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 · 2018-04-02T06:50:49

The time is $= 5.46 s$ $=5.46s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(4 - 5)}^{2} + {(9 - 2)}^{2} + {(8 - 1)}^{2}} = \sqrt{1 + 49 + 49} = \sqrt{99} m$ $AB=sqrt((4-5)^2+(9-2)^2+(8-1)^2)=sqrt(1+49+49)=sqrt(99)m$

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 $a = \frac{2}{3} m s^{- 2}$ $a=2/3ms^-2$

Therefore,

$\sqrt{99} = 0 + \frac{1}{2} \cdot \frac{2}{3} \cdot t^{2}$ $sqrt99=0+1/2*2/3*t^2$

$t^{2} = 3 \cdot \sqrt{99}$ $t^2=3*sqrt99$

$t = \sqrt{3 \cdot \sqrt{99}} = 5.46 s$ $t=sqrt(3*sqrt99)=5.46s$

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An object is at rest at $(5, 2, 1)$ $(5 ,2 ,1 )$ and constantly accelerates at a rate of $\frac{2}{3} \frac{m}{s}$ $2/3 m/s$ as it moves to point B. If point B is at $(4, 9, 8)$ $(4 ,9 ,8 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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Explanation:

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An object is at rest at (5,2,1)(5 ,2 ,1 ) and constantly accelerates at a rate of 23ms2/3 m/s as it moves to point B. If point B is at (4,9,8)(4 ,9 ,8 ), 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 $(5, 2, 1)$ $(5 ,2 ,1 )$ and constantly accelerates at a rate of $\frac{2}{3} \frac{m}{s}$ $2/3 m/s$ as it moves to point B. If point B is at $(4, 9, 8)$ $(4 ,9 ,8 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.