# An object is at rest at (1 ,5 ,5 ) and constantly accelerates at a rate of 7/4 ms^-2 as it moves to point B. If point B is at (2 ,5 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Aug 1, 2016

The distance to be covered is $\sqrt{2}$ $m$, and this takes $0.96$ $s$.

#### Explanation:

First find the distance to be covered:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

$d = \sqrt{{\left(2 - 1\right)}^{2} + {\left(5 - 5\right)}^{2} + {\left(6 - 5\right)}^{2}} = \sqrt{{1}^{2} + {0}^{2} + {1}^{2}} = \sqrt{2}$ $m$

Now we can use the equation:

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

But the initial velocity $u = 0$, so $s = \frac{1}{2} a {t}^{2}$

Rearranging to make $t$ the subject:

$t = \sqrt{\frac{2 s}{a}} = \frac{\sqrt{2 \times \sqrt{2}}}{\frac{7}{4}} = 0.96$ $s$.