An object is at rest at $(8, 9, 2)$ $(8 ,9 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s}$ $4/3 m/s$ as it moves to point B. If point B is at $(3, 1, 6)$ $(3 ,1 ,6 )$ , 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 $(8, 9, 2)$ $(8 ,9 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s}$ $4/3 m/s$ as it moves to point B. If point B is at $(3, 1, 6)$ $(3 ,1 ,6 )$ , 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 · 2018-04-08T09:02:53

The time is $= 3.92 s$ $=3.92s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(3 - 8)}^{2} + {(1 - 9)}^{2} + {(6 - 2)}^{2}} = \sqrt{25 + 64 + 16} = \sqrt{105} m$ $AB=sqrt((3-8)^2+(1-9)^2+(6-2)^2)=sqrt(25+64+16)=sqrt(105)m$

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 $a = \frac{4}{3} m s^{- 2}$ $a=4/3ms^-2$

Therefore,

$\sqrt{105} = 0 + \frac{1}{2} \cdot \frac{4}{3} \cdot t^{2}$ $sqrt105=0+1/2*4/3*t^2$

$t^{2} = \frac{3}{2} \cdot \sqrt{105}$ $t^2=3/2*sqrt105$

$t = \sqrt{\frac{3}{2} \cdot \sqrt{105}} = 3.92 s$ $t=sqrt(3/2*sqrt105)=3.92s$

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An object is at rest at $(8, 9, 2)$ $(8 ,9 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s}$ $4/3 m/s$ as it moves to point B. If point B is at $(3, 1, 6)$ $(3 ,1 ,6 )$ , 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 (8,9,2)(8 ,9 ,2 ) and constantly accelerates at a rate of 43ms4/3 m/s as it moves to point B. If point B is at (3,1,6)(3 ,1 ,6 ), 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 $(8, 9, 2)$ $(8 ,9 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s}$ $4/3 m/s$ as it moves to point B. If point B is at $(3, 1, 6)$ $(3 ,1 ,6 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.