An object is at rest at $(5, 2, 8)$ $(5 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Question

An object is at rest at $(5, 2, 8)$ $(5 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer

Impact of this question

1387 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-26T07:37:51

The time is $= 7.85 s$ $=7.85s$

Explanation:

The distance $A B$ $AB$ is

$A B = \sqrt{{(6 - 5)}^{2} + {(3 - 2)}^{2} + {(2 - 8)}^{2}} = \sqrt{1 + 1 + 36} = (\sqrt{38}) m$ $AB=sqrt((6-5)^2+(3-2)^2+(2-8)^2)=sqrt(1+1+36)=(sqrt38)m$

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 $a = \frac{1}{5} m s^{- 2}$ $a=1/5ms^-2$

Therefore,

$\sqrt{38} = 0 \cdot \frac{1}{2} \cdot \frac{1}{5} \cdot t^{2}$ $sqrt38=0*1/2*1/5*t^2$

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

$t = \sqrt{10 \sqrt{38}} = 7.85 s$ $t=sqrt(10sqrt38)=7.85s$

Science

Math

Humanities

... and beyond

An object is at rest at $(5, 2, 8)$ $(5 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

An object is at rest at (5 ,2 ,8 )(5,2,8)(5 ,2 ,8 ) and constantly accelerates at a rate of 1/5 m/s15ms1/5 m/s as it moves to point B. If point B is at (6 ,3 ,2 )(6,3,2)(6 ,3 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer

Explanation:

Related questions

Impact of this question

An object is at rest at $(5, 2, 8)$ $(5 ,2 ,8 )$ and constantly accelerates at a rate of $\frac{1}{5} \frac{m}{s}$ $1/5 m/s$ as it moves to point B. If point B is at $(6, 3, 2)$ $(6 ,3 ,2 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.