hard acceleration question help. (1 Viewer)

[posh bitch]

someone please explain this question to me. i dont understand it

 

[Zenox]

<a href="http://www.codecogs.com/eqnedit.php?latex=\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} @plus; K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} @plus; K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} + K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} + K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" title="\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} + K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} + K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" /></a>

should be 160000/10000

 

[Zenox]

<a href="http://www.codecogs.com/eqnedit.php?latex=\\v=0~,~when ~Rocket~ is ~at~ rest \\As~x \to \infty ~,~v\rightarrow 0 \\ v\neq 0 \\Thus, ~rocket~ never ~comes ~to ~rest" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\\v=0~,~when ~Rocket~ is ~at~ rest \\As~x \to \infty ~,~v\rightarrow 0 \\ v\neq 0 \\Thus, ~rocket~ never ~comes ~to ~rest" title="\\v=0~,~when ~Rocket~ is ~at~ rest \\As~x \to \infty ~,~v\rightarrow 0 \\ v\neq 0 \\Thus, ~rocket~ never ~comes ~to ~rest" /></a>

 

[Skeptyks]

<a href="http://www.codecogs.com/eqnedit.php?latex=\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} @plus; K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} @plus; K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} + K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} + K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" title="\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} + K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} + K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" /></a>

You're trying to write dv^2/d^2x right? not dx2 o_o

 

[Zenox]

You're trying to write dv^2/d^2x right? not dx2 o_o

This,

<a href="http://www.codecogs.com/eqnedit.php?latex=a = \frac{d}{dx}\left (\frac{1}{2}v^2 \right )" target="_blank"><img src="http://latex.codecogs.com/gif.latex?a = \frac{d}{dx}\left (\frac{1}{2}v^2 \right )" title="a = \frac{d}{dx}\left (\frac{1}{2}v^2 \right )" /></a>

 

[Skeptyks]

This,

<a href="http://www.codecogs.com/eqnedit.php?latex=a = \frac{d}{dx}\left (\frac{1}{2}v^2 \right )" target="_blank"><img src="http://latex.codecogs.com/gif.latex?a = \frac{d}{dx}\left (\frac{1}{2}v^2 \right )" title="a = \frac{d}{dx}\left (\frac{1}{2}v^2 \right )" /></a>

o right my bad haha
what i was thinking was dx^2/d^2t zzz

 

[posh bitch]

<a href="http://www.codecogs.com/eqnedit.php?latex=\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} @plus; K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} @plus; K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} + K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} + K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" title="\dpi{80} a=\frac{-80000}{x^2}~,~a=\frac{dv^2}{dx2} \\\\ \frac{dv^2}{dx2}=\frac{-80000}{x^2}~~ \rightarrow ~~\frac{v^2}{2} = \int -8000x^{-2} ~dx \\ \frac{v^2}{2} = \frac{80000}{x} + K \\\\Applying~Initial~Conditions~,v=5,x=6400 \\ \frac{25}{2}=\frac{80000}{6400} + K \\ K=0\\\frac{v^2}{2}=\frac{80000}{x} ~\rightarrow ~v^2=\frac{160000}{x}\\When~rocket~ is~ at~ surface~ of~ the~ Earth~,~x=10000\\v^2=\frac{16000}{10000}=16\\v^2=16\\v=4~,~v> 0" /></a>

should be 160000/10000

Thank you so much for this and the second part x