An object is at rest at $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(3, 1, 4)$ $(3 ,1 ,4 )$ , 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 $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(3, 1, 4)$ $(3 ,1 ,4 )$ , 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 · 2018-03-27T08:11:24

$t = 3.24$ $t=3.24$

Explanation:

You can use the formula $s = u t + \frac{1}{2} (a t^{2})$ $s=ut+1/2(at^2)$
$u$ $u$ is initial velocity
$s$ $s$ is distance travelled
$t$ $t$ is time
$a$ $a$ is acceleration

Now, it starts from rest so initial velocity is 0

$s = \frac{1}{2} (a t^{2})$ $s=1/2(at^2)$

To find s between $(6, 7, 2)$ $(6,7,2)$ and $(3, 1, 4)$ $(3,1,4)$
We use distance formula
$s = \sqrt{{(6 - 3)}^{2} + {(7 - 1)}^{2} + {(2 - 4)}^{2}}$ $s=sqrt((6-3)^2+(7-1)^2+(2-4)^2)$
$s = \sqrt{9 + 36 + 4}$ $s=sqrt(9+36+4)$
$s = 7$ $s=7$

Acceleration is $\frac{4}{3}$ $4/3$ meters per second per second

$7 = \frac{1}{2} ((\frac{4}{3}) t^{2})$ $7=1/2((4/3)t^2)$
$14 \cdot (\frac{3}{4}) = t^{2}$ $14*(3/4)=t^2$
$t = \sqrt{10.5} = 3.24$ $t=sqrt(10.5)=3.24$

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An object is at rest at $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(3, 1, 4)$ $(3 ,1 ,4 )$ , 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 (6,7,2)(6 ,7 ,2 ) and constantly accelerates at a rate of 43ms24/3 m/s^2 as it moves to point B. If point B is at (3,1,4)(3 ,1 ,4 ), 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 $(6, 7, 2)$ $(6 ,7 ,2 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(3, 1, 4)$ $(3 ,1 ,4 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.