An object is at rest at $(2, 4, 2)$ $(2 ,4 ,2 )$ and constantly accelerates at a rate of $\frac{4}{5} \frac{m}{s}$ $4/5 m/s$ as it moves to point B. If point B is at $(3, 6, 9)$ $(3 ,6 ,9 )$ , 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 $(2, 4, 2)$ $(2 ,4 ,2 )$ and constantly accelerates at a rate of $\frac{4}{5} \frac{m}{s}$ $4/5 m/s$ as it moves to point B. If point B is at $(3, 6, 9)$ $(3 ,6 ,9 )$ , 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 · 2017-09-14T09:30:43

The time is $= 4.79 s$ $=4.79s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(3 - 2)}^{2} + {(6 - 4)}^{2} + {(9 - 2)}^{2}} = \sqrt{{(1)}^{2} + {(2)}^{2} + {(7)}^{2}}$ $AB=sqrt((3-2)^2+(6-4)^2+(9-2)^2)=sqrt((1)^2+(2)^2+(7)^2)$

$= \sqrt{1 + 4 + 49} = \sqrt{54} m$ $=sqrt(1+4+49)=sqrt54m$

The acceleration is $a = \frac{4}{5} m s^{- 2}$ $a=4/5ms^-2$

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,

$\sqrt{54} = 0 + \frac{1}{2} \cdot {(\frac{4}{5})}^{2} \cdot t^{2}$ $sqrt54=0+1/2*(4/5)^2*t^2$

$t^{2} = \frac{50}{16} \sqrt{54}$ $t^2=50/16sqrt54$

$t = \sqrt{\frac{50}{16} \sqrt{54}} = 4.79 s$ $t=sqrt(50/16sqrt54)=4.79s$

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An object is at rest at $(2, 4, 2)$ $(2 ,4 ,2 )$ and constantly accelerates at a rate of $\frac{4}{5} \frac{m}{s}$ $4/5 m/s$ as it moves to point B. If point B is at $(3, 6, 9)$ $(3 ,6 ,9 )$ , 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 (2,4,2)(2 ,4 ,2 ) and constantly accelerates at a rate of 45ms4/5 m/s as it moves to point B. If point B is at (3,6,9)(3 ,6 ,9 ), 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 $(2, 4, 2)$ $(2 ,4 ,2 )$ and constantly accelerates at a rate of $\frac{4}{5} \frac{m}{s}$ $4/5 m/s$ as it moves to point B. If point B is at $(3, 6, 9)$ $(3 ,6 ,9 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.