An object is at rest at $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $2 \frac{m}{s}$ $2 m/s$ as it moves to point B. If point B is at $(6, 7, 7)$ $(6 ,7 ,7 )$ , 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 $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $2 \frac{m}{s}$ $2 m/s$ as it moves to point B. If point B is at $(6, 7, 7)$ $(6 ,7 ,7 )$ , 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 · 2018-04-21T06:06:31

The time is $= 2.74 s$ $=2.74s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(6 - 2)}^{2} + {(7 - 1)}^{2} + {(7 - 5)}^{2}} = \sqrt{16 + 36 + 4} = \sqrt{56} m$ $AB=sqrt((6-2)^2+(7-1)^2+(7-5)^2)=sqrt(16+36+4)=sqrt(56)m$

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 $a = 2 m s^{- 2}$ $a=2ms^-2$

Therefore,

$\sqrt{56} = 0 + \frac{1}{2} \cdot 2 \cdot t^{2}$ $sqrt56=0+1/2*2*t^2$

$t^{2} = \sqrt{56}$ $t^2=sqrt56$

$t = \sqrt{\sqrt{56}} = 2.74 s$ $t=sqrt(sqrt56)=2.74s$

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An object is at rest at $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $2 \frac{m}{s}$ $2 m/s$ as it moves to point B. If point B is at $(6, 7, 7)$ $(6 ,7 ,7 )$ , 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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1 Answer

Explanation:

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