An object is at rest at $(2, 2, 8)$ $(2 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , 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 $(2, 2, 8)$ $(2 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , 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 · 2018-02-21T07:15:50

The time is $= 12.07 s$ $=12.07s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(6 - 2)}^{2} + {(3 - 2)}^{2} + {(2 - 8)}^{2}} = \sqrt{16 + 1 + 36} = \sqrt{53} m$ $AB=sqrt((6-2)^2+(3-2)^2+(2-8)^2)=sqrt(16+1+36)=sqrt(53)m$

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 $a = \frac{1}{5} m s^{- 2}$ $a=1/5ms^-2$

Therefore,

$\sqrt{53} = 0 + \frac{1}{2} \cdot \frac{1}{5} \cdot t^{2}$ $sqrt53=0+1/2*1/5*t^2$

$t^{2} = 20 \cdot \sqrt{53}$ $t^2=20*sqrt53$

$t = \sqrt{20 \cdot \sqrt{53}} = 12.07 s$ $t=sqrt(20*sqrt53)=12.07s$

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An object is at rest at $(2, 2, 8)$ $(2 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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Explanation:

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An object is at rest at (2,2,8)(2 ,2 ,8 ) and constantly accelerates at a rate of 15ms1/5 m/s as it moves to point B. If point B is at (6,3,2)(6 ,3 ,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 $(2, 2, 8)$ $(2 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.