An object is at rest at $(4, 1, 2)$ $(4 ,1 ,2 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(5, 6, 1)$ $(5 ,6 ,1 )$ , 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 $(4, 1, 2)$ $(4 ,1 ,2 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(5, 6, 1)$ $(5 ,6 ,1 )$ , 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 · 2018-02-02T06:39:40

The time is $= 2.72 s$ $=2.72s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(5 - 4)}^{2} + {(6 - 1)}^{2} + {(1 - 2)}^{2}} = \sqrt{1 + 25 + 1} = \sqrt{27} m$ $AB=sqrt((5-4)^2+(6-1)^2+(1-2)^2)=sqrt(1+25+1)=sqrt(27)m$

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 $a = \frac{7}{5} m s^{- 2}$ $a=7/5ms^-2$

Therefore,

$\sqrt{27} = 0 + \frac{1}{2} \cdot \frac{7}{5} \cdot t^{2}$ $sqrt27=0+1/2*7/5*t^2$

$t^{2} = \frac{10}{7} \cdot \sqrt{27}$ $t^2=10/7*sqrt27$

$t = \sqrt{\frac{10}{7} \cdot \sqrt{26}} = 2.72 s$ $t=sqrt(10/7*sqrt26)=2.72s$

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An object is at rest at $(4, 1, 2)$ $(4 ,1 ,2 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(5, 6, 1)$ $(5 ,6 ,1 )$ , 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 (4 ,1 ,2 )(4,1,2)(4 ,1 ,2 ) and constantly accelerates at a rate of 7/5 m/s^275ms27/5 m/s^2 as it moves to point B. If point B is at (5 ,6 ,1 )(5,6,1)(5 ,6 ,1 ), 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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Impact of this question

An object is at rest at $(4, 1, 2)$ $(4 ,1 ,2 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(5, 6, 1)$ $(5 ,6 ,1 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.