# 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 ,3 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Aug 6, 2016

First find the distance between the points, then use $s = u t + \frac{1}{2} a {t}^{2}$ to find the time taken.

#### Explanation:

First find the distance between the points:

$r = \sqrt{{\left(2 - 1\right)}^{2} + {\left(3 - 5\right)}^{2} + {\left(6 - 1\right)}^{2}} = \sqrt{6} \approx 2.45$ $m$

Now use the formula:

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

The initial velocity, $u = 0$ $m {s}^{-} 1$, so $s = \frac{1}{2} a {t}^{2}$. We can rearrange to make $t$ the subject:

$t = \sqrt{\frac{2 s}{a}} = \sqrt{\frac{2 \times 2.45}{\frac{7}{4}}} = \sqrt{2.8} \approx 1.67$ $s$