An object is at rest at $(4, 5, 8)$ $(4 ,5 ,8 )$ and constantly accelerates at a rate of $\frac{4}{3} \frac{m}{s^{2}}$ $4/3 m/s^2$ as it moves to point B. If point B is at $(7, 9, 2)$ $(7 ,9 ,2 )$ , 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 · 2016-05-09T13:04:45

Find the distance, define the motion and from the equation of motion you can find the time. Answer is:

$t = 3.423$ $t=3.423$ $s$ $s$

Firstly, you have to find the distance. The Cartesian distance in 3D environments is:

$Δs=sqrt(Δx^2+Δy^2+Δz^2)$

Assuming the coordinates are in form of $(x,y,z)$

$Δs=sqrt((4-7)^2+(5-9)^2+(8-2)^2)$

$Δs=7.81$ $m$

The motion is acceleration. Therefore:

$s=s_0+u_0*t+1/2*a*t^2$

The object starts still $(u_0=0)$ and the distance is $Δs=s-s_0$

$s-s_0=u_0*t+1/2*a*t^2$

$Δs=u_0*t+1/2*a*t^2$

$7.81=0*t+1/2*4/3*t^2$

$t=sqrt((3*7.81)/2)$

$t=3.423$ $s$

An object is at rest at (4 ,5 ,8 )(4,5,8)(4 ,5 ,8 ) and constantly accelerates at a rate of 4/3 m/s^243ms24/3 m/s^2 as it moves to point B. If point B is at (7 ,9 ,2 )(7,9,2)(7 ,9 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.