How Do You Calculate Position, Velocity, and Acceleration from d(x)/d(t) = c/x?

[69911e]

I have the equation v=c/x
d(x)/d(t)=c/x
velocity= c(constant)/x (distance)

I need equations to calculate position, velocity and acceleration for a given time,
My attempt was:
xdx=cdt
x²ln(x)=ct
e^lnxx2=e^kt
x^x2=e^kt
but I need x(t)v(t),a(t)

Any suggestions on how to calculate?

 

[JorisL]

You start of well with $xdx = cdt$
The next step is wrong. How do you justify $\int xdx = x^2 \text{ln}(x)$?
Because that's what happens there.

If you know $x(t)$ how can you find $v(t)$ and $a(t)$?

Spoiler

You've already used how you get $v(t)$

 

[HomogenousCow]

Where did the ln(x) come from??

 

[69911e]

Where did the ln(x) come from??

I did int of XDx= x²*(Dx/x)=
x²LN(x)

That was the wrong move...

Thanks

 

[Mark44]

I have the equation v=c/x
d(x)/d(t)=c/x

Usually, posters don't include enough parentheses, but here you have more than you need, which might have led to some confusion.

The above can be written as $\frac{dx}{dt} = \frac c x$. Separating, we get x dx = c dt. Integrating, we get $\frac 1 2 x^2 = ct + K$.

velocity= c(constant)/x (distance)

I need equations to calculate position, velocity and acceleration for a given time,
My attempt was:
xdx=cdt
x²ln(x)=ct
e^lnxx2=e^kt
x^x2=e^kt
but I need x(t)v(t),a(t)

Any suggestions on how to calculate?