An object is at rest at (2 ,9 ,5 ) and constantly accelerates at a rate of 1/5 m/s as it moves to point B. If point B is at (6 ,2 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Jul 29, 2017

$t = 9.11$ $\text{s}$

Explanation:

NOTE: I'll assume the given acceleration is $\frac{1}{5}$ ${\text{m/s}}^{2}$, not $\frac{1}{5}$ $\text{m/s}$.

We're asked to find the time $t$ it takes an object to travel a certain distance with a given constant acceleration.

To do this, we can use the equation

$\Delta x = {v}_{0 x} t + \frac{1}{2} {a}_{x} {t}^{2}$

where

• $\Delta x$ is the distance it travels, which can be found using the distance formula:

$\Delta x = \sqrt{{\left(6 - 2\right)}^{2} + {\left(2 - 9\right)}^{2} + {\left(7 - 5\right)}^{2}} = 8.31$ $\text{m}$

• ${v}_{0 x}$ is the initial velocity, which is $0$ since it started from rest

• $t$ is the time (we're trying to find this)

• ${a}_{x}$ is the constant acceleration (given as $\frac{1}{5}$ ${\text{m/s}}^{2}$)

Plugging in known values, we have

$8.31$ $\text{m}$ $= 0 t + \frac{1}{2} \left(\frac{1}{5} \textcolor{w h i t e}{l} {\text{m/s}}^{2}\right) {t}^{2}$

t = sqrt((8.31color(white)(l)"m")/(1/10color(white)(l)"m/s"^2)) = color(red)(ul(9.11color(white)(l)"s"