# An object is at rest at (7 ,3 ,9 ) and constantly accelerates at a rate of 7/4 m/s^2 as it moves to point B. If point B is at (2 ,5 ,0 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Jun 10, 2018

The time is $= 3.46 s$

#### Explanation:

The distance $A B$ is

$| | \vec{A B} | | = \sqrt{{\left(2 - 7\right)}^{2} + {\left(5 - 3\right)}^{2} + {\left(0 - 9\right)}^{2}} = \sqrt{25 + 4 + 81} = \sqrt{110} m$

Apply the equation of motion

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

The initial velocity is $u = 0 m {s}^{-} 1$

The acceleration is $a = \frac{7}{4} m {s}^{-} 2$

Therefore,

$\sqrt{110} = 0 + \frac{1}{2} \cdot \frac{7}{4} \cdot {t}^{2}$

${t}^{2} = \frac{8}{7} \sqrt{110}$

$t = \sqrt{\frac{8}{7} \sqrt{110}} = 3.46 s$

The time is $= 3.46 s$