An object is at rest at $(2, 1, 6)$ $(2 ,1 ,6 )$ and constantly accelerates at a rate of $\frac{1}{4} \frac{m}{s^{2}}$ $1/4 m/s^2$ as it moves to point B. If point B is at $(6, 4, 5)$ $(6 ,4 ,5 )$ , 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 $(2, 1, 6)$ $(2 ,1 ,6 )$ and constantly accelerates at a rate of $\frac{1}{4} \frac{m}{s^{2}}$ $1/4 m/s^2$ as it moves to point B. If point B is at $(6, 4, 5)$ $(6 ,4 ,5 )$ , 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 · 2017-07-20T15:03:43

The time is $= 6.39 s$ $=6.39s$

Explanation:

The distance is

$s = \sqrt{{(6 - 2)}^{2} + {(4 - 1)}^{2} + {(5 - 6)}^{2}}$ $s=sqrt((6-2)^2+(4-1)^2+(5-6)^2)$

$= \sqrt{16 + 9 + 1}$ $=sqrt(16+9+1)$

$= \sqrt{26} m$ $=sqrt26m$

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

The acceleration is $= \frac{1}{4} m s^{- 2}$ $=1/4ms^-2$

We apply the equation of motion

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

$t = \sqrt{\frac{2 s}{a}}$ $t=sqrt((2s)/a)$

$t = \sqrt{\frac{2 \cdot \sqrt{26}}{\frac{1}{4}}}$ $t=sqrt((2*sqrt26)/(1/4))$

$t = 6.39 s$ $t=6.39s$

Answer 2 · 2017-07-20T15:06:44

$6.387$ $6.387$ seconds

Explanation:

The distance between $(2, 1, 6)$ $(2,1,6)$ and $6, 4, 5)$ $6,4,5)$ is

$\sqrt{{(6 - 2)}^{2} + {(4 - 1)}^{2} + {(5 - 6)}^{2}} = \sqrt{16 + 9 + 1} = \sqrt{26}$ $sqrt((6-2)^2+(4-1)^2+(5-6)^2)=sqrt(16+9+1)=sqrt26$ , and it is in meters.

As distance $S = \frac{1}{2} a t^{2}$ $S=1/2at^2$ , where $a$ $a$ is accelaration and $t$ $t$ is time taken, then

$t = \sqrt{\frac{2 S}{a}} = \sqrt{\frac{2 \sqrt{26}}{\frac{1}{4}}}$ $t=sqrt((2S)/a)=sqrt((2sqrt26)/(1/4))$

= $\sqrt{8 \sqrt{26}} = 2 \sqrt{2 \times 5.09902} = 2 \sqrt{10.19804} = 6.387$ $sqrt(8sqrt26)=2sqrt(2xx5.09902)=2sqrt10.19804=6.387$

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An object is at rest at $(2, 1, 6)$ $(2 ,1 ,6 )$ and constantly accelerates at a rate of $\frac{1}{4} \frac{m}{s^{2}}$ $1/4 m/s^2$ as it moves to point B. If point B is at $(6, 4, 5)$ $(6 ,4 ,5 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.

2 Answers

Explanation:

Explanation:

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An object is at rest at (2,1,6)(2 ,1 ,6 ) and constantly accelerates at a rate of 14ms21/4 m/s^2 as it moves to point B. If point B is at (6,4,5)(6 ,4 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

2 Answers

Explanation:

Explanation:

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An object is at rest at $(2, 1, 6)$ $(2 ,1 ,6 )$ and constantly accelerates at a rate of $\frac{1}{4} \frac{m}{s^{2}}$ $1/4 m/s^2$ as it moves to point B. If point B is at $(6, 4, 5)$ $(6 ,4 ,5 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.