An object is at rest at $(8, 3, 6)$ $(8 ,3 ,6 )$ 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 $(6, 8, 2)$ $(6 ,8 ,2 )$ , 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 $(8, 3, 6)$ $(8 ,3 ,6 )$ 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 $(6, 8, 2)$ $(6 ,8 ,2 )$ , 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 · 2016-06-25T05:33:25

It will take $4.23$ $4.23$ seconds.

Explanation:

The distance between two points $(x_{1}, y_{1}, z_{1})$ $(x_1,y_1,z_1)$ and $(x_{2}, y_{2}, z_{2})$ $(x_2,y_2,z_2)$ is given by

$\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2} + {(z_{2} - z_{1})}_{2}^{2}}$ $sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$

Hence distance between $(8, 3, 6)$ $(8,3,6)$ and $(6, 8, 2)$ $(6,8,2)$ is

$\sqrt{{(8 - 6)}^{2} + {(3 - 8)}^{2} + {(6 - 2)}^{2}}$ $sqrt((8-6)^2+(3-8)^2+(6-2)^2)$

= $\sqrt{2^{2} + 5^{2} + 4^{2}} = \sqrt{4 + 25 + 16} = \sqrt{45} = 3 \sqrt{5}$ $sqrt(2^2+5^2+4^2)=sqrt(4+25+16)=sqrt45=3sqrt5$

(As distance covered is given by $S = u t + \frac{1}{2} a t^{2}$ $S=ut+1/2at^2$ , where $u$ $u$ is initial velocity, $a$ $a$ is accelaration and $t$ $t$ is time taken. If body is at rest $S = \frac{1}{2} a t^{2}$ $S=1/2at^2$ and hence $t = \sqrt{\frac{2 S}{a}}$ $t=sqrt((2S)/a)$

As the coordinates are in meters, the time taken at an acceleration of $\frac{1}{4}$ $1/4$ $\frac{m}{{sec}^{2}}$ $m/sec^2$ will be given by

$t = \sqrt{\frac{2 \times 3 \sqrt{5}}{\frac{1}{4}}} = \sqrt{4 \times 2 \times 2.236} = \sqrt{17.888} = 4.23$ $t=sqrt((2xx3sqrt5)/(1/4))=sqrt(4xx2xx2.236)=sqrt(17.888)=4.23$

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An object is at rest at $(8, 3, 6)$ $(8 ,3 ,6 )$ 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 $(6, 8, 2)$ $(6 ,8 ,2 )$ , 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 (8,3,6)(8 ,3 ,6 ) and constantly accelerates at a rate of 14ms21/4 m/s^2 as it moves to point B. If point B is at (6,8,2)(6 ,8 ,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 $(8, 3, 6)$ $(8 ,3 ,6 )$ 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 $(6, 8, 2)$ $(6 ,8 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.