An object is at rest at $(7, 9, 4)$ $(7 ,9 ,4 )$ and constantly accelerates at a rate of $\frac{7}{4} \frac{m}{s^{2}}$ $7/4 m/s^2$ as it moves to point B. If point B is at $(5, 1, 8)$ $(5 ,1 ,8 )$ , 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 · 2017-06-13T22:55:39

$t = 3.24$ $t = 3.24$ $s$ $"s"$

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

We can use the equation

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

where

$Deltax$ is the change in position of the object, which is simply the distance between the two coordinate points:

$Deltax = sqrt((5"m" - 7"m")^2 + (1"m" - 9"m")^2 + (8"m" - 4"m")^2)$

$= 9.17$ $"m"$

Plugging in known variables we have

$9.17"m" = (0)t + 1/2(7/4"m/s"^2)t^2$

$9.17"m" = (7/8"m/s"^2)t^2$

$t^2 = (9.16"m")/(7/8"m/s"^2)$

$t = sqrt((9.16"m")/(7/8"m/s"^2)) = color(red)(3.24$ $color(red)("s"$

The object will travel the distance in $color(red)(3.24$ seconds

An object is at rest at (7 ,9 ,4 )(7,9,4)(7 ,9 ,4 ) and constantly accelerates at a rate of 7/4 m/s^274ms27/4 m/s^2 as it moves to point B. If point B is at (5 ,1 ,8 )(5,1,8)(5 ,1 ,8 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.