# 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.

##### 1 Answer
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