An object is at rest at $(9, 1, 3)$ $(9 ,1 ,3 )$ 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 $(9, 1, 3)$ $(9 ,1 ,3 )$ 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 · 2017-08-11T06:18:10

The time is $= 15.7 s$ $=15.7s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(6 - 9)}^{2} + {(8 - 1)}^{2} + {(2 - 3)}^{2}} = \sqrt{{(- 3)}^{2} + {(7)}^{2} + {(- 1)}^{2}}$ $AB=sqrt((6-9)^2+(8-1)^2+(2-3)^2)=sqrt((-3)^2+(7)^2+(-1)^2)$

$= \sqrt{9 + 49 + 1} = \sqrt{59} m$ $=sqrt(9+49+1)=sqrt59m$

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

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

We apply the equation of motion

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

So,

$\sqrt{59} = 0 + \frac{1}{2} \cdot {(\frac{1}{4})}^{2} \cdot t^{2}$ $sqrt59=0+1/2*(1/4)^2*t^2$

$t^{2} = 32 \sqrt{59}$ $t^2=32sqrt59$

$t = \sqrt{32 \sqrt{59}} = 15.7 s$ $t=sqrt(32sqrt59)=15.7s$

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An object is at rest at $(9, 1, 3)$ $(9 ,1 ,3 )$ 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 (9,1,3)(9 ,1 ,3 ) 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 $(9, 1, 3)$ $(9 ,1 ,3 )$ 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.