An object is at rest at $(2, 1, 5)$ $(2 ,1 ,5 )$ and constantly accelerates at a rate of $\frac{7}{6} \frac{m}{s}$ $7/6 m/s$ as it moves to point B. If point B is at $(6, 3, 7)$ $(6 ,3 ,7 )$ , 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 · 2017-07-31T03:56:31

$t = 2.90$ $t = 2.90$ $s$ $"s"$

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:

$Deltax = sqrt((2-6)^2 + (1-3)^2 + (5-7)^2) = 4.90$ $"m"$

Plugging in known values, we have

$4.90$ $"m"$ $=0t + 1/2(7/6color(white)(l)"m/s"^2)t^2$

$t = sqrt((4.90color(white)(l)"m")/(7/12color(white)(l)"m/s"^2)) = color(red)(ul(2.90color(white)(l)"s"$

An object is at rest at (2 ,1 ,5 )(2,1,5)(2 ,1 ,5 ) and constantly accelerates at a rate of 7/6 m/s76ms7/6 m/s as it moves to point B. If point B is at (6 ,3 ,7 )(6,3,7)(6 ,3 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.