An object is at rest at $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(8, 1, 7)$ $(8 ,1 ,7 )$ , 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 $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(8, 1, 7)$ $(8 ,1 ,7 )$ , 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 · 2016-03-19T15:41:34

$\approx 3.46 s$ $~~3.46s$

Explanation:

Here displacement = linear distance between the given points
so displacement $s = \sqrt{{(6 - 8)}^{2} + {(7 - 1)}^{2} + {(2 - 7)}^{2}} = \sqrt{65} m$ $s=sqrt((6-8)^2+(7-1)^2+(2-7)^2)=sqrt65m$
Initial velocity $u = 0$ $u=0$
Acceleration $a = \frac{4}{3} m s^{- 2}$ $a=4/3ms^-2$
time taken t=?

So $s = u t + \frac{1}{2} a t^{2}$ $s=ut+1/2at^2$
$\sqrt{65} = 0 \cdot t + \frac{1}{2} \cdot \frac{4}{3} t^{2}$ $sqrt65=0*t+1/2*4/3t^2$
$t^{2} = \frac{3}{2} \cdot \sqrt{65} \approx 12$ $t^2=3/2*sqrt65~~12$
$t \approx \sqrt{12} \approx 3.46 s$ $t ~~sqrt12~~3.46s$

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An object is at rest at $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(8, 1, 7)$ $(8 ,1 ,7 )$ , 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 (6,7,2)(6 ,7 ,2 ) and constantly accelerates at a rate of 43ms24/3 m/s^2 as it moves to point B. If point B is at (8,1,7)(8 ,1 ,7 ), 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 $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(8, 1, 7)$ $(8 ,1 ,7 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.