An object is at rest at (8 ,2 ,5 ) and constantly accelerates at a rate of 7/4 m/s^2 as it moves to point B. If point B is at (6 ,5 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Apr 7, 2017

The time is $= 4.71 s$

Explanation:

The distance between the 2 points $A \left(8 , 2 , 5\right)$ and $B \left(6 , 5 , 7\right)$ is

$s = \sqrt{{\left(6 - 8\right)}^{2} + {\left(5 - 2\right)}^{2} + {\left(7 - 5\right)}^{2}}$

$s = \sqrt{4 + 9 + 4}$

$s = \sqrt{17} m$

We apply the equation of motion

$s = u t + \frac{1}{2} a {t}^{2}$

initial velocity, $u = 0 m {s}^{-} 1$

acceleration, $a = \frac{7}{4} m {s}^{-} 2$

distance, $s = \sqrt{17} m$

so,

$\sqrt{17} = 0 + \frac{1}{2} \cdot \frac{7}{4} \cdot t$

$t = \frac{8}{7} \sqrt{17} = 4.71 s$