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

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Answer 1 · 2017-07-29T19:47:06

$t = 9.11$ $t = 9.11$ $s$ $"s"$

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

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

To do this, we can use the equation

$Deltax = v_(0x)t + 1/2a_xt^2$

where

$Deltax$ is the distance it travels, which can be found using the distance formula:

$Deltax = sqrt((6-2)^2 + (2-9)^2 + (7-5)^2) = 8.31$ $"m"$

Plugging in known values, we have

$8.31$ $"m"$ $=0t + 1/2(1/5color(white)(l)"m/s"^2)t^2$

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

An object is at rest at (2 ,9 ,5 )(2,9,5)(2 ,9 ,5 ) and constantly accelerates at a rate of 1/5 m/s15ms1/5 m/s as it moves to point B. If point B is at (6 ,2 ,7 )(6,2,7)(6 ,2 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.