# An object is at rest at (8 ,4 ,2 ) and constantly accelerates at a rate of 4/3 m/s as it moves to point B. If point B is at (3 ,1 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

##### 1 Answer
Mar 6, 2017

$\sqrt{\frac{21}{2}} s$

#### Explanation:

let initial point A be (8,4,2) and final point B be (3,1,6)

by distance formula,

= $\sqrt{{\left(8 - 3\right)}^{2} + {\left(4 - 1\right)}^{2} + {\left(2 - 6\right)}^{2}}$

$\therefore$ distance 's' between A and B is $\sqrt{50}$

So, s = $\sqrt{50}$ = $5 \sqrt{2}$ = $5 \cdot 1.41$ = 7m approx

also,
as object is at rest and starts constantly accelerating,
initial velocity ' u' = 0

By using equation,
s = ut + $\frac{1}{2} a {t}^{2}$

as u = 0, s = $\frac{1}{2} a {t}^{2}$

7 = $\frac{1}{2} \cdot \frac{4}{3} {t}^{2}$

t = $\sqrt{\frac{21}{2}}$s