An object is at rest at (1 ,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 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Mar 23, 2016

The distance between the points (calculated below) is $3.74$ $m$. Then $d = u t + \frac{1}{2} a {t}^{2} = 0 \left(t\right) + \frac{1}{2} \left(\frac{7}{4}\right) {t}^{2.}$ Rearranging, $\frac{7}{8} {t}^{2} = 3.74 \to t = 2.1 s$.
$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$
$= \sqrt{{\left(2 - 1\right)}^{2} + {\left(5 - 3\right)}^{2} + {\left(6 - 9\right)}^{2}}$
$= \sqrt{1 + 4 + 9} = \sqrt{14} \approx 3.74$ $m$.