# An object is at rest at (9 ,7 ,5 ) and constantly accelerates at a rate of 5/4 m/s^2 as it moves to point B. If point B is at (1 ,2 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Oct 12, 2017

$t \approx 3.98 \text{ s}$

#### Explanation:

Compute the distance from point A to point B:

$d = \sqrt{{\left(9 - 1\right)}^{2} + {\left(7 - 2\right)}^{2} + {\left(5 - 2\right)}^{2}}$

$d = 7 \sqrt{2} \text{ m}$

To find the time, $t$, taken to travel a distance, $d$, given the constant acceleration, we shall use the equation:

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

Solve for t:

$t = \sqrt{2 \frac{d}{a}}$

Substitute $d = 7 \sqrt{2} \text{ m}$ and $a = \frac{5}{4} {\text{ m/s}}^{2}$ into the equation:

$t = \sqrt{2 \left(7 \sqrt{2} {\text{ m")/(5/4" m/s}}^{2}\right)}$

$t \approx 3.98 \text{ s}$