An object is at rest at $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $3 \frac{m}{s}$ $3 m/s$ as it moves to point B. If point B is at $(6, 7, 5)$ $(6 ,7 ,5 )$ , 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 $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $3 \frac{m}{s}$ $3 m/s$ as it moves to point B. If point B is at $(6, 7, 5)$ $(6 ,7 ,5 )$ , 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 · 2016-06-24T05:37:13

It will take $2.193$ $2.193$ 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 $(2, 1, 5)$ $(2,1,5)$ and $(6, 7, 5)$ $(6,7,5)$ is

$\sqrt{{(6 - 2)}^{2} + {(7 - 1)}^{2} + {(5 - 5)}^{2}}$ $sqrt((6-2)^2+(7-1)^2+(5-5)^2)$

= $\sqrt{4^{2} + 6^{2} + 0^{2}} = \sqrt{16 + 36 + 0} = \sqrt{52} = 2 \sqrt{13}$ $sqrt(4^2+6^2+0^2)=sqrt(16+36+0)=sqrt52=2sqrt13$

(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 $3$ $3$ $\frac{m}{{sec}^{2}}$ $m/sec^2$ will be given by

$t = \sqrt{\frac{2 \times 2 \sqrt{13}}{3}} = \sqrt{\frac{4 \times 3.606}{3}} = \sqrt{4.808} = 2.193$ $t=sqrt((2xx2sqrt13)/3)=sqrt((4xx3.606)/3)=sqrt(4.808)=2.193$

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An object is at rest at $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $3 \frac{m}{s}$ $3 m/s$ as it moves to point B. If point B is at $(6, 7, 5)$ $(6 ,7 ,5 )$ , 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 (2,1,5)(2 ,1 ,5 ) and constantly accelerates at a rate of 3ms3 m/s as it moves to point B. If point B is at (6,7,5)(6 ,7 ,5 ), 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 $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $3 \frac{m}{s}$ $3 m/s$ as it moves to point B. If point B is at $(6, 7, 5)$ $(6 ,7 ,5 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.