An object is at rest at $(7, 6, 4)$ $(7 ,6 ,4 )$ and constantly accelerates at a rate of $\frac{7}{4} \frac{m}{s^{2}}$ $7/4 m/s^2$ as it moves to point B. If point B is at $(5, 1, 7)$ $(5 ,1 ,7 )$ , 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 $(7, 6, 4)$ $(7 ,6 ,4 )$ and constantly accelerates at a rate of $\frac{7}{4} \frac{m}{s^{2}}$ $7/4 m/s^2$ as it moves to point B. If point B is at $(5, 1, 7)$ $(5 ,1 ,7 )$ , 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 · 2018-01-30T10:42:52

The time is $= 2.65 s$ $=2.65s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(5 - 7)}^{2} + {(1 - 6)}^{2} + {(7 - 4)}^{2}} = \sqrt{4 + 25 + 9} = \sqrt{38} m$ $AB=sqrt((5-7)^2+(1-6)^2+(7-4)^2)=sqrt(4+25+9)=sqrt(38)m$

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 $a = \frac{7}{4} m s^{- 2}$ $a=7/4ms^-2$

Therefore,

$\sqrt{38} = 0 + \frac{1}{2} \cdot \frac{7}{4} \cdot t^{2}$ $sqrt38=0+1/2*7/4*t^2$

$t^{2} = \frac{8}{7} \cdot \sqrt{38}$ $t^2=8/7*sqrt38$

$t = \sqrt{\frac{8}{7} \cdot \sqrt{38}} = 2.65 s$ $t=sqrt(8/7*sqrt38)=2.65s$

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An object is at rest at $(7, 6, 4)$ $(7 ,6 ,4 )$ and constantly accelerates at a rate of $\frac{7}{4} \frac{m}{s^{2}}$ $7/4 m/s^2$ as it moves to point B. If point B is at $(5, 1, 7)$ $(5 ,1 ,7 )$ , 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 (7,6,4)(7 ,6 ,4 ) and constantly accelerates at a rate of 74ms27/4 m/s^2 as it moves to point B. If point B is at (5,1,7)(5 ,1 ,7 ), 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 $(7, 6, 4)$ $(7 ,6 ,4 )$ and constantly accelerates at a rate of $\frac{7}{4} \frac{m}{s^{2}}$ $7/4 m/s^2$ as it moves to point B. If point B is at $(5, 1, 7)$ $(5 ,1 ,7 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.