# An object is at rest at (6 ,7 ,2 ) and constantly accelerates at a rate of 4/3 m/s^2 as it moves to point B. If point B is at (8 ,1 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Mar 19, 2016

$\approx 3.46 s$

#### Explanation:

Here displacement = linear distance between the given points
so displacement $s = \sqrt{{\left(6 - 8\right)}^{2} + {\left(7 - 1\right)}^{2} + {\left(2 - 7\right)}^{2}} = \sqrt{65} m$
Initial velocity $u = 0$
Acceleration $a = \frac{4}{3} m {s}^{-} 2$
time taken t=?

So $s = u t + \frac{1}{2} a {t}^{2}$
$\sqrt{65} = 0 \cdot t + \frac{1}{2} \cdot \frac{4}{3} {t}^{2}$
${t}^{2} = \frac{3}{2} \cdot \sqrt{65} \approx 12$
$t \approx \sqrt{12} \approx 3.46 s$