An object is at rest at $(4, 1, 8)$ $(4 ,1 ,8 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(2, 9, 1)$ $(2 ,9 ,1 )$ , 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 $(4, 1, 8)$ $(4 ,1 ,8 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(2, 9, 1)$ $(2 ,9 ,1 )$ , 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 · 2017-11-29T19:13:22

The time is $= 3.93 s$ $=3.93s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(2 - 4)}^{2} + {(9 - 1)}^{2} + {(1 - 8)}^{2}} = \sqrt{4 + 64 + 49} = (\sqrt{117}) m$ $AB=sqrt((2-4)^2+(9-1)^2+(1-8)^2)=sqrt(4+64+49)=(sqrt117)m$

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 $a = \frac{7}{5} m s^{- 2}$ $a=7/5ms^-2$

Therefore,

$\sqrt{117} = 0 \cdot \frac{1}{2} \cdot \frac{7}{5} \cdot t^{2}$ $sqrt117=0*1/2*7/5*t^2$

$t^{2} = \frac{10}{7} \sqrt{117}$ $t^2=10/7sqrt117$

$t = \sqrt{\frac{10}{7} \sqrt{117}} = 3.93 s$ $t=sqrt(10/7sqrt117)=3.93s$

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An object is at rest at $(4, 1, 8)$ $(4 ,1 ,8 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(2, 9, 1)$ $(2 ,9 ,1 )$ , 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 (4,1,8)(4 ,1 ,8 ) and constantly accelerates at a rate of 75ms27/5 m/s^2 as it moves to point B. If point B is at (2,9,1)(2 ,9 ,1 ), 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 $(4, 1, 8)$ $(4 ,1 ,8 )$ and constantly accelerates at a rate of $\frac{7}{5} \frac{m}{s^{2}}$ $7/5 m/s^2$ as it moves to point B. If point B is at $(2, 9, 1)$ $(2 ,9 ,1 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.