An object is at rest at (8 ,7 ,3 ) and constantly accelerates at a rate of 1/4 m/s^2 as it moves to point B. If point B is at (1 ,3 ,4 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Mar 29, 2016

$t = 8 , 06 \text{ s}$

Explanation:

"Point A=(8,7,3) Point B=(1,3,4")
$\text{distance between the Point A and B :}$

$s = \sqrt{{\left(1 - 8\right)}^{2} + {\left(3 - 7\right)}^{2} + {\left(4 - 3\right)}^{2}}$

$s = \sqrt{{\left(- 7\right)}^{2} + {\left(- 4\right)}^{2} + {1}^{2}}$

$s = \sqrt{49 + 16 + 1} \text{ } s = \sqrt{66}$

$s = 8 , 12 \text{ m}$

$\text{equation for an object constantly accelerating from rest}$

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

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

$a = \frac{1}{4} \text{ } \frac{m}{s} ^ 2$

${t}^{2} = \frac{2 \cdot 8 , 12}{\frac{1}{4}}$

${t}^{2} = 2 \cdot 8 , 12 \cdot 4 = 64 , 96$

$t = 8 , 06 \text{ s}$