# An object is at rest at (7 ,3 ,9 ) and constantly accelerates at a rate of 7/4 ms^-2 as it moves to point B. If point B is at (2 ,5 ,8 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Jan 23, 2018

First we find the distance between the points, which is $5.5$ m, then calculate the time taken, which is $2.5$ s.

#### Explanation:

Find the distance between the points:

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

$s = \sqrt{{\left(7 - 2\right)}^{2} + {\left(5 - 3\right)}^{2} + {\left(9 - 8\right)}^{2}}$

$s = \sqrt{{5}^{2} + {2}^{2} + {1}^{2}} = \sqrt{30} = 5.5$ m

Now to find the time taken:

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

The initial velocity, $u$, is just equal to $0$ because the object is initially at rest, so this reduces to:

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

$t = \sqrt{\frac{2 s}{a}} = \sqrt{\frac{2 \times 5.5}{\frac{7}{4}}} = 2.5$ s