An object is at rest at $(8, 7, 3)$ $(8 ,7 ,3 )$ 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 $(1, 3, 2)$ $(1 ,3 ,2 )$ , 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 $(8, 7, 3)$ $(8 ,7 ,3 )$ 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 $(1, 3, 2)$ $(1 ,3 ,2 )$ , 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 · 2017-12-12T06:26:28

The time is $= 8.06 s$ $=8.06s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(1 - 8)}^{2} + {(3 - 7)}^{2} + {(2 - 3)}^{2}} = \sqrt{49 + 16 + 1} = (\sqrt{66}) m$ $AB=sqrt((1-8)^2+(3-7)^2+(2-3)^2)=sqrt(49+16+1)=(sqrt66)m$

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

Therefore,

$\sqrt{66} = 0 + \frac{1}{2} \cdot \frac{1}{4} \cdot t^{2}$ $sqrt66=0+1/2*1/4*t^2$

$t^{2} = 8 \sqrt{66}$ $t^2=8sqrt66$

$t = \sqrt{8 \sqrt{66}} = 8.06 s$ $t=sqrt(8sqrt66)=8.06s$

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An object is at rest at $(8, 7, 3)$ $(8 ,7 ,3 )$ 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 $(1, 3, 2)$ $(1 ,3 ,2 )$ , 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 (8,7,3)(8 ,7 ,3 ) and constantly accelerates at a rate of 14ms21/4 m/s^2 as it moves to point B. If point B is at (1,3,2)(1 ,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 $(8, 7, 3)$ $(8 ,7 ,3 )$ 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 $(1, 3, 2)$ $(1 ,3 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.