An object is at rest at $(4, 7, 3)$ $(4 ,7 ,3 )$ 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 $(5, 6, 9)$ $(5 ,6 ,9 )$ , 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 $(4, 7, 3)$ $(4 ,7 ,3 )$ 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 $(5, 6, 9)$ $(5 ,6 ,9 )$ , 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 · 2018-01-03T07:25:52

The time is $= 3.0 s$ $=3.0s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(5 - 4)}^{2} + {(6 - 7)}^{2} + {(9 - 3)}^{2}} = \sqrt{1 + 1 + 36} = (\sqrt{38}) m$ $AB=sqrt((5-4)^2+(6-7)^2+(9-3)^2)=sqrt(1+1+36)=(sqrt38)m$

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,

$\sqrt{38} = 0 + \frac{1}{2} \cdot \frac{7}{5} \cdot t^{2}$ $sqrt(38)=0+1/2*7/5*t^2$

$t^{2} = \frac{10}{7} \sqrt{38}$ $t^2=10/7sqrt38$

$t = \sqrt{\frac{10}{7} \sqrt{38}} = 3.0 s$ $t=sqrt(10/7sqrt38)=3.0s$

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An object is at rest at $(4, 7, 3)$ $(4 ,7 ,3 )$ 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 $(5, 6, 9)$ $(5 ,6 ,9 )$ , 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 (4,7,3)(4 ,7 ,3 ) and constantly accelerates at a rate of 75ms27/5 m/s^2 as it moves to point B. If point B is at (5,6,9)(5 ,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 $(4, 7, 3)$ $(4 ,7 ,3 )$ 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 $(5, 6, 9)$ $(5 ,6 ,9 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.